120646
If tangents are drawn from any point on the circle \(x^2+y^2=25\) to the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\) then the angle between the tangents is
1 \(\frac{2 \pi}{3}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
Explanation:
D Given,
\(x^2+y^2=25=16+9\)
\(\therefore \mathrm{x}^2+\mathrm{y}^2=\mathrm{a}^2+\mathrm{b}^2\) is director circle of the ellipse
So, the angle between the tangents is \(\frac{\pi}{2}\)
AP EAMCET-2014
Ellipse
120650
If \(P\) is a variable point on the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), with \(A A^{\prime}\) as major axis. Then, the maximum value of the area of the \(\triangle \mathrm{APA}^{\prime}\) is
1 ab sq unit
2 2 ab sq unit
3 \(\frac{a b}{2}\) squnit
4 None of these
Explanation:
A The maximum area corresponds to when \(\mathrm{P}\) is at either end of the minor axis.
\(\therefore\) Required area \(=\frac{1}{2}(2 a) b=a b\) squnit
Manipal UGET-2012
Ellipse
120636
The locus of the point of intersection of perpendicular tangents to the ellipse is called
1 director circle
2 hyperbola
3 ellipse
4 auxiliary circle
Explanation:
A We know that, locus of point of intersection of perpendicular tangents to the ellipse is called "director circle".
120646
If tangents are drawn from any point on the circle \(x^2+y^2=25\) to the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\) then the angle between the tangents is
1 \(\frac{2 \pi}{3}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
Explanation:
D Given,
\(x^2+y^2=25=16+9\)
\(\therefore \mathrm{x}^2+\mathrm{y}^2=\mathrm{a}^2+\mathrm{b}^2\) is director circle of the ellipse
So, the angle between the tangents is \(\frac{\pi}{2}\)
AP EAMCET-2014
Ellipse
120650
If \(P\) is a variable point on the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), with \(A A^{\prime}\) as major axis. Then, the maximum value of the area of the \(\triangle \mathrm{APA}^{\prime}\) is
1 ab sq unit
2 2 ab sq unit
3 \(\frac{a b}{2}\) squnit
4 None of these
Explanation:
A The maximum area corresponds to when \(\mathrm{P}\) is at either end of the minor axis.
\(\therefore\) Required area \(=\frac{1}{2}(2 a) b=a b\) squnit
Manipal UGET-2012
Ellipse
120636
The locus of the point of intersection of perpendicular tangents to the ellipse is called
1 director circle
2 hyperbola
3 ellipse
4 auxiliary circle
Explanation:
A We know that, locus of point of intersection of perpendicular tangents to the ellipse is called "director circle".
120646
If tangents are drawn from any point on the circle \(x^2+y^2=25\) to the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\) then the angle between the tangents is
1 \(\frac{2 \pi}{3}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
Explanation:
D Given,
\(x^2+y^2=25=16+9\)
\(\therefore \mathrm{x}^2+\mathrm{y}^2=\mathrm{a}^2+\mathrm{b}^2\) is director circle of the ellipse
So, the angle between the tangents is \(\frac{\pi}{2}\)
AP EAMCET-2014
Ellipse
120650
If \(P\) is a variable point on the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), with \(A A^{\prime}\) as major axis. Then, the maximum value of the area of the \(\triangle \mathrm{APA}^{\prime}\) is
1 ab sq unit
2 2 ab sq unit
3 \(\frac{a b}{2}\) squnit
4 None of these
Explanation:
A The maximum area corresponds to when \(\mathrm{P}\) is at either end of the minor axis.
\(\therefore\) Required area \(=\frac{1}{2}(2 a) b=a b\) squnit
Manipal UGET-2012
Ellipse
120636
The locus of the point of intersection of perpendicular tangents to the ellipse is called
1 director circle
2 hyperbola
3 ellipse
4 auxiliary circle
Explanation:
A We know that, locus of point of intersection of perpendicular tangents to the ellipse is called "director circle".
