120555
If \(S\) and \(S^{\prime}\) are the foci of the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\), and \(P\) is any point on it, then range of values of SP. S'P is
120556
The radius of the circle passing through the focii of the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\), and having its centre at \((0,3)\) is
1 4
2 3
3 \(\sqrt{12}\)
4 \(7 / 2\)
Explanation:
A Given,
\(\frac{x^2}{16}+\frac{y^2}{9}=1, \text { centre }(0,3)\)
\(a=4, b=3, e=\sqrt{1-\frac{b^2}{a^2}}=\frac{\sqrt{7}}{4}\)
Radius \((\mathrm{r})=\sqrt{(\mathrm{ae})^2+\mathrm{b}^2}\)
\(r=\sqrt{\left(4 \times \frac{\sqrt{7}}{4}\right)^2+(3)^2}\)
\(r=\sqrt{7+9}=\sqrt{16}\)
\(r=4\)
AMU-2008
Ellipse
120557
If a point \(P(x, y)\) moves along the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\) and if \(c\) is the center of the ellipse, then the sum of maximum and minimum values of \(\mathrm{CP}\) is \(\qquad\)
1 25
2 9
3 4
4 5
Explanation:
B Given that,
\(\frac{x^2}{25}+\frac{y^2}{16}=1\)
Equation of ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
On comparing equation (i) and (ii), we get
\(a^2=25 \Rightarrow a= \pm 5\)
\(b^2=16 \Rightarrow b= \pm 4\)
Maximum value of \(\mathrm{CP}\) is where \(\mathrm{CP}=5\) unit Minimum value of \(\mathrm{CP}\) is where \(\mathrm{CP}=4 \mathrm{unit}\) So, sum of maximum and minimum value of \(\mathrm{CP}\) is
\(=5+4\)
\(=9 \text { unit }\)
AP EAMCET-19.08.2021
Ellipse
120558
If the major axis of an ellipse lies on the \(Y\)-axis, its minor axis lies on the \(\mathrm{X}\)-axis and the length of its latus rectum is equal to \(\frac{2}{3}\) of its minor axis, then the eccentricity of that ellipse is
120559
\(S\) and \(T\) are the foci of an ellipse and \(B\) is an end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is
120555
If \(S\) and \(S^{\prime}\) are the foci of the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\), and \(P\) is any point on it, then range of values of SP. S'P is
120556
The radius of the circle passing through the focii of the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\), and having its centre at \((0,3)\) is
1 4
2 3
3 \(\sqrt{12}\)
4 \(7 / 2\)
Explanation:
A Given,
\(\frac{x^2}{16}+\frac{y^2}{9}=1, \text { centre }(0,3)\)
\(a=4, b=3, e=\sqrt{1-\frac{b^2}{a^2}}=\frac{\sqrt{7}}{4}\)
Radius \((\mathrm{r})=\sqrt{(\mathrm{ae})^2+\mathrm{b}^2}\)
\(r=\sqrt{\left(4 \times \frac{\sqrt{7}}{4}\right)^2+(3)^2}\)
\(r=\sqrt{7+9}=\sqrt{16}\)
\(r=4\)
AMU-2008
Ellipse
120557
If a point \(P(x, y)\) moves along the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\) and if \(c\) is the center of the ellipse, then the sum of maximum and minimum values of \(\mathrm{CP}\) is \(\qquad\)
1 25
2 9
3 4
4 5
Explanation:
B Given that,
\(\frac{x^2}{25}+\frac{y^2}{16}=1\)
Equation of ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
On comparing equation (i) and (ii), we get
\(a^2=25 \Rightarrow a= \pm 5\)
\(b^2=16 \Rightarrow b= \pm 4\)
Maximum value of \(\mathrm{CP}\) is where \(\mathrm{CP}=5\) unit Minimum value of \(\mathrm{CP}\) is where \(\mathrm{CP}=4 \mathrm{unit}\) So, sum of maximum and minimum value of \(\mathrm{CP}\) is
\(=5+4\)
\(=9 \text { unit }\)
AP EAMCET-19.08.2021
Ellipse
120558
If the major axis of an ellipse lies on the \(Y\)-axis, its minor axis lies on the \(\mathrm{X}\)-axis and the length of its latus rectum is equal to \(\frac{2}{3}\) of its minor axis, then the eccentricity of that ellipse is
120559
\(S\) and \(T\) are the foci of an ellipse and \(B\) is an end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is
120555
If \(S\) and \(S^{\prime}\) are the foci of the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\), and \(P\) is any point on it, then range of values of SP. S'P is
120556
The radius of the circle passing through the focii of the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\), and having its centre at \((0,3)\) is
1 4
2 3
3 \(\sqrt{12}\)
4 \(7 / 2\)
Explanation:
A Given,
\(\frac{x^2}{16}+\frac{y^2}{9}=1, \text { centre }(0,3)\)
\(a=4, b=3, e=\sqrt{1-\frac{b^2}{a^2}}=\frac{\sqrt{7}}{4}\)
Radius \((\mathrm{r})=\sqrt{(\mathrm{ae})^2+\mathrm{b}^2}\)
\(r=\sqrt{\left(4 \times \frac{\sqrt{7}}{4}\right)^2+(3)^2}\)
\(r=\sqrt{7+9}=\sqrt{16}\)
\(r=4\)
AMU-2008
Ellipse
120557
If a point \(P(x, y)\) moves along the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\) and if \(c\) is the center of the ellipse, then the sum of maximum and minimum values of \(\mathrm{CP}\) is \(\qquad\)
1 25
2 9
3 4
4 5
Explanation:
B Given that,
\(\frac{x^2}{25}+\frac{y^2}{16}=1\)
Equation of ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
On comparing equation (i) and (ii), we get
\(a^2=25 \Rightarrow a= \pm 5\)
\(b^2=16 \Rightarrow b= \pm 4\)
Maximum value of \(\mathrm{CP}\) is where \(\mathrm{CP}=5\) unit Minimum value of \(\mathrm{CP}\) is where \(\mathrm{CP}=4 \mathrm{unit}\) So, sum of maximum and minimum value of \(\mathrm{CP}\) is
\(=5+4\)
\(=9 \text { unit }\)
AP EAMCET-19.08.2021
Ellipse
120558
If the major axis of an ellipse lies on the \(Y\)-axis, its minor axis lies on the \(\mathrm{X}\)-axis and the length of its latus rectum is equal to \(\frac{2}{3}\) of its minor axis, then the eccentricity of that ellipse is
120559
\(S\) and \(T\) are the foci of an ellipse and \(B\) is an end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is
120555
If \(S\) and \(S^{\prime}\) are the foci of the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\), and \(P\) is any point on it, then range of values of SP. S'P is
120556
The radius of the circle passing through the focii of the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\), and having its centre at \((0,3)\) is
1 4
2 3
3 \(\sqrt{12}\)
4 \(7 / 2\)
Explanation:
A Given,
\(\frac{x^2}{16}+\frac{y^2}{9}=1, \text { centre }(0,3)\)
\(a=4, b=3, e=\sqrt{1-\frac{b^2}{a^2}}=\frac{\sqrt{7}}{4}\)
Radius \((\mathrm{r})=\sqrt{(\mathrm{ae})^2+\mathrm{b}^2}\)
\(r=\sqrt{\left(4 \times \frac{\sqrt{7}}{4}\right)^2+(3)^2}\)
\(r=\sqrt{7+9}=\sqrt{16}\)
\(r=4\)
AMU-2008
Ellipse
120557
If a point \(P(x, y)\) moves along the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\) and if \(c\) is the center of the ellipse, then the sum of maximum and minimum values of \(\mathrm{CP}\) is \(\qquad\)
1 25
2 9
3 4
4 5
Explanation:
B Given that,
\(\frac{x^2}{25}+\frac{y^2}{16}=1\)
Equation of ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
On comparing equation (i) and (ii), we get
\(a^2=25 \Rightarrow a= \pm 5\)
\(b^2=16 \Rightarrow b= \pm 4\)
Maximum value of \(\mathrm{CP}\) is where \(\mathrm{CP}=5\) unit Minimum value of \(\mathrm{CP}\) is where \(\mathrm{CP}=4 \mathrm{unit}\) So, sum of maximum and minimum value of \(\mathrm{CP}\) is
\(=5+4\)
\(=9 \text { unit }\)
AP EAMCET-19.08.2021
Ellipse
120558
If the major axis of an ellipse lies on the \(Y\)-axis, its minor axis lies on the \(\mathrm{X}\)-axis and the length of its latus rectum is equal to \(\frac{2}{3}\) of its minor axis, then the eccentricity of that ellipse is
120559
\(S\) and \(T\) are the foci of an ellipse and \(B\) is an end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is
120555
If \(S\) and \(S^{\prime}\) are the foci of the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\), and \(P\) is any point on it, then range of values of SP. S'P is
120556
The radius of the circle passing through the focii of the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\), and having its centre at \((0,3)\) is
1 4
2 3
3 \(\sqrt{12}\)
4 \(7 / 2\)
Explanation:
A Given,
\(\frac{x^2}{16}+\frac{y^2}{9}=1, \text { centre }(0,3)\)
\(a=4, b=3, e=\sqrt{1-\frac{b^2}{a^2}}=\frac{\sqrt{7}}{4}\)
Radius \((\mathrm{r})=\sqrt{(\mathrm{ae})^2+\mathrm{b}^2}\)
\(r=\sqrt{\left(4 \times \frac{\sqrt{7}}{4}\right)^2+(3)^2}\)
\(r=\sqrt{7+9}=\sqrt{16}\)
\(r=4\)
AMU-2008
Ellipse
120557
If a point \(P(x, y)\) moves along the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\) and if \(c\) is the center of the ellipse, then the sum of maximum and minimum values of \(\mathrm{CP}\) is \(\qquad\)
1 25
2 9
3 4
4 5
Explanation:
B Given that,
\(\frac{x^2}{25}+\frac{y^2}{16}=1\)
Equation of ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
On comparing equation (i) and (ii), we get
\(a^2=25 \Rightarrow a= \pm 5\)
\(b^2=16 \Rightarrow b= \pm 4\)
Maximum value of \(\mathrm{CP}\) is where \(\mathrm{CP}=5\) unit Minimum value of \(\mathrm{CP}\) is where \(\mathrm{CP}=4 \mathrm{unit}\) So, sum of maximum and minimum value of \(\mathrm{CP}\) is
\(=5+4\)
\(=9 \text { unit }\)
AP EAMCET-19.08.2021
Ellipse
120558
If the major axis of an ellipse lies on the \(Y\)-axis, its minor axis lies on the \(\mathrm{X}\)-axis and the length of its latus rectum is equal to \(\frac{2}{3}\) of its minor axis, then the eccentricity of that ellipse is
120559
\(S\) and \(T\) are the foci of an ellipse and \(B\) is an end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is
