Tangent and Normal of Parabola
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Parabola

120300 Let \(R\) be the focus of the parabola \(y^2=20 x\) and the line \(\mathbf{y}=\mathbf{m x}+\mathbf{c}\) intersect the parabola at two points \(P\) and \(Q\). Let the point \(G(10,10)\) be the centroid of the triangle \(P Q R\). If \(c-m=6\), then \((\mathrm{PQ})^2\) is

1 325
2 317
3 296
4 346
JEE Main-08.04.2023
Parabola

120301 The equation of the tangent to \(y=-2 x^2+3\) at \(x\) \(=1\) is

1 \(y=-4 x\)
2 \(y=-4 x+5\)
3 \(y=4 x\)
4 \(y=4 x+5\)
5 \(y=4 x+3\)
Kerala CEE-2020
Parabola

120302 If the line \(y=k x\) touches the parabola \(y=(x-\) \(1)^2\), then the values of \(k\) are

1 \(2,-2\)
2 0,4
3 \(0,-2\)
4 0,2
5 \(0,-4\)
Kerala CEE-2015
Parabola

120303 The condition that \(a x+b y+c=0\) is tangent to the parabola \(y^2=4 \mathrm{ax}\), is:

1 \(\mathrm{a}^2=\mathrm{b}^2=\mathrm{c}^2\)
2 \(a=b\)
3 \(b^2=\mathrm{c}\)
4 \(\mathrm{b}^2=\mathrm{a}\)
5 \(\mathrm{a}^2=\mathrm{b}\)
Kerala CEE-2004
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Parabola

120300 Let \(R\) be the focus of the parabola \(y^2=20 x\) and the line \(\mathbf{y}=\mathbf{m x}+\mathbf{c}\) intersect the parabola at two points \(P\) and \(Q\). Let the point \(G(10,10)\) be the centroid of the triangle \(P Q R\). If \(c-m=6\), then \((\mathrm{PQ})^2\) is

1 325
2 317
3 296
4 346
JEE Main-08.04.2023
Parabola

120301 The equation of the tangent to \(y=-2 x^2+3\) at \(x\) \(=1\) is

1 \(y=-4 x\)
2 \(y=-4 x+5\)
3 \(y=4 x\)
4 \(y=4 x+5\)
5 \(y=4 x+3\)
Kerala CEE-2020
Parabola

120302 If the line \(y=k x\) touches the parabola \(y=(x-\) \(1)^2\), then the values of \(k\) are

1 \(2,-2\)
2 0,4
3 \(0,-2\)
4 0,2
5 \(0,-4\)
Kerala CEE-2015
Parabola

120303 The condition that \(a x+b y+c=0\) is tangent to the parabola \(y^2=4 \mathrm{ax}\), is:

1 \(\mathrm{a}^2=\mathrm{b}^2=\mathrm{c}^2\)
2 \(a=b\)
3 \(b^2=\mathrm{c}\)
4 \(\mathrm{b}^2=\mathrm{a}\)
5 \(\mathrm{a}^2=\mathrm{b}\)
Kerala CEE-2004
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Parabola

120300 Let \(R\) be the focus of the parabola \(y^2=20 x\) and the line \(\mathbf{y}=\mathbf{m x}+\mathbf{c}\) intersect the parabola at two points \(P\) and \(Q\). Let the point \(G(10,10)\) be the centroid of the triangle \(P Q R\). If \(c-m=6\), then \((\mathrm{PQ})^2\) is

1 325
2 317
3 296
4 346
JEE Main-08.04.2023
Parabola

120301 The equation of the tangent to \(y=-2 x^2+3\) at \(x\) \(=1\) is

1 \(y=-4 x\)
2 \(y=-4 x+5\)
3 \(y=4 x\)
4 \(y=4 x+5\)
5 \(y=4 x+3\)
Kerala CEE-2020
Parabola

120302 If the line \(y=k x\) touches the parabola \(y=(x-\) \(1)^2\), then the values of \(k\) are

1 \(2,-2\)
2 0,4
3 \(0,-2\)
4 0,2
5 \(0,-4\)
Kerala CEE-2015
Parabola

120303 The condition that \(a x+b y+c=0\) is tangent to the parabola \(y^2=4 \mathrm{ax}\), is:

1 \(\mathrm{a}^2=\mathrm{b}^2=\mathrm{c}^2\)
2 \(a=b\)
3 \(b^2=\mathrm{c}\)
4 \(\mathrm{b}^2=\mathrm{a}\)
5 \(\mathrm{a}^2=\mathrm{b}\)
Kerala CEE-2004
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Parabola

120300 Let \(R\) be the focus of the parabola \(y^2=20 x\) and the line \(\mathbf{y}=\mathbf{m x}+\mathbf{c}\) intersect the parabola at two points \(P\) and \(Q\). Let the point \(G(10,10)\) be the centroid of the triangle \(P Q R\). If \(c-m=6\), then \((\mathrm{PQ})^2\) is

1 325
2 317
3 296
4 346
JEE Main-08.04.2023
Parabola

120301 The equation of the tangent to \(y=-2 x^2+3\) at \(x\) \(=1\) is

1 \(y=-4 x\)
2 \(y=-4 x+5\)
3 \(y=4 x\)
4 \(y=4 x+5\)
5 \(y=4 x+3\)
Kerala CEE-2020
Parabola

120302 If the line \(y=k x\) touches the parabola \(y=(x-\) \(1)^2\), then the values of \(k\) are

1 \(2,-2\)
2 0,4
3 \(0,-2\)
4 0,2
5 \(0,-4\)
Kerala CEE-2015
Parabola

120303 The condition that \(a x+b y+c=0\) is tangent to the parabola \(y^2=4 \mathrm{ax}\), is:

1 \(\mathrm{a}^2=\mathrm{b}^2=\mathrm{c}^2\)
2 \(a=b\)
3 \(b^2=\mathrm{c}\)
4 \(\mathrm{b}^2=\mathrm{a}\)
5 \(\mathrm{a}^2=\mathrm{b}\)
Kerala CEE-2004