Tangent and Normal of Parabola
Parabola

120304 The common tangent of the parabolas \(y^2=4 x\) and \(x^2=-8 y\) is

1 \(y=x+2\)
2 \(y=x-2\)
3 \(y=2 x+3\)
4 None of these
Parabola

120305 The equations of the sides \(A B\) and \(A C\) of a triangle \(A B C\) are \((\lambda+1) x+\lambda y=4\) and \(\lambda x+(1\) \(-\lambda) \mathbf{y}+\lambda=0\) respectively. Its vertex \(A\) is on the \(y\)-axis and its orthocenter is \((1,2)\). The length of the tangent from the point \(C\) to the part of the parabola \(\mathrm{y}^2=6 \mathrm{x}\) in the first quadrant is :

1 \(2 \sqrt{2}\)
2 2
3 \(\sqrt{6}\)
4 4
Parabola

120989 The line \(4 x+6 y+9=0\) touches \(y^2=4 a x\) at the point

1 \((-3,9 / 4)\)
2 \((-3,-9 / 4)\)
3 \((9 / 4,-3)\)
4 \((-9 / 4,-3)\)
Parabola

120990 The slopes of the normal to the parabola \(y^2=\) 4ax intersecting at a point on the axis of the parabola at a distance 4 a from its vertex are in

1 A.P.
2 G.P.
3 H.P.
4 none of these
Parabola

120304 The common tangent of the parabolas \(y^2=4 x\) and \(x^2=-8 y\) is

1 \(y=x+2\)
2 \(y=x-2\)
3 \(y=2 x+3\)
4 None of these
Parabola

120305 The equations of the sides \(A B\) and \(A C\) of a triangle \(A B C\) are \((\lambda+1) x+\lambda y=4\) and \(\lambda x+(1\) \(-\lambda) \mathbf{y}+\lambda=0\) respectively. Its vertex \(A\) is on the \(y\)-axis and its orthocenter is \((1,2)\). The length of the tangent from the point \(C\) to the part of the parabola \(\mathrm{y}^2=6 \mathrm{x}\) in the first quadrant is :

1 \(2 \sqrt{2}\)
2 2
3 \(\sqrt{6}\)
4 4
Parabola

120989 The line \(4 x+6 y+9=0\) touches \(y^2=4 a x\) at the point

1 \((-3,9 / 4)\)
2 \((-3,-9 / 4)\)
3 \((9 / 4,-3)\)
4 \((-9 / 4,-3)\)
Parabola

120990 The slopes of the normal to the parabola \(y^2=\) 4ax intersecting at a point on the axis of the parabola at a distance 4 a from its vertex are in

1 A.P.
2 G.P.
3 H.P.
4 none of these
Parabola

120304 The common tangent of the parabolas \(y^2=4 x\) and \(x^2=-8 y\) is

1 \(y=x+2\)
2 \(y=x-2\)
3 \(y=2 x+3\)
4 None of these
Parabola

120305 The equations of the sides \(A B\) and \(A C\) of a triangle \(A B C\) are \((\lambda+1) x+\lambda y=4\) and \(\lambda x+(1\) \(-\lambda) \mathbf{y}+\lambda=0\) respectively. Its vertex \(A\) is on the \(y\)-axis and its orthocenter is \((1,2)\). The length of the tangent from the point \(C\) to the part of the parabola \(\mathrm{y}^2=6 \mathrm{x}\) in the first quadrant is :

1 \(2 \sqrt{2}\)
2 2
3 \(\sqrt{6}\)
4 4
Parabola

120989 The line \(4 x+6 y+9=0\) touches \(y^2=4 a x\) at the point

1 \((-3,9 / 4)\)
2 \((-3,-9 / 4)\)
3 \((9 / 4,-3)\)
4 \((-9 / 4,-3)\)
Parabola

120990 The slopes of the normal to the parabola \(y^2=\) 4ax intersecting at a point on the axis of the parabola at a distance 4 a from its vertex are in

1 A.P.
2 G.P.
3 H.P.
4 none of these
Parabola

120304 The common tangent of the parabolas \(y^2=4 x\) and \(x^2=-8 y\) is

1 \(y=x+2\)
2 \(y=x-2\)
3 \(y=2 x+3\)
4 None of these
Parabola

120305 The equations of the sides \(A B\) and \(A C\) of a triangle \(A B C\) are \((\lambda+1) x+\lambda y=4\) and \(\lambda x+(1\) \(-\lambda) \mathbf{y}+\lambda=0\) respectively. Its vertex \(A\) is on the \(y\)-axis and its orthocenter is \((1,2)\). The length of the tangent from the point \(C\) to the part of the parabola \(\mathrm{y}^2=6 \mathrm{x}\) in the first quadrant is :

1 \(2 \sqrt{2}\)
2 2
3 \(\sqrt{6}\)
4 4
Parabola

120989 The line \(4 x+6 y+9=0\) touches \(y^2=4 a x\) at the point

1 \((-3,9 / 4)\)
2 \((-3,-9 / 4)\)
3 \((9 / 4,-3)\)
4 \((-9 / 4,-3)\)
Parabola

120990 The slopes of the normal to the parabola \(y^2=\) 4ax intersecting at a point on the axis of the parabola at a distance 4 a from its vertex are in

1 A.P.
2 G.P.
3 H.P.
4 none of these