Let '$$d$$' be the perpendicular distance from the centre of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ to the tangent drawn at a point $$P$$ on the ellipse. If $${F_1}$$ and $${F_2}$$ are the two foci of the ellipse, then show that $${\left( {P{F_1} - P{F_2}} \right)^2} = 4{a^2}\left( {1 - {{{b^2}} \over {{d^2}}}} \right)$$.
Answer
Solve it.
2
IIT-JEE 1995
Subjective
Show that the locus of a point that divides a chord of slope $$2$$ of the parabola $${y^2} = 4x$$ internally in the ratio $$1:2$$ is a parabola. Find the vertex of this parabola.
Answer
$$\left( {{2 \over 9},{8 \over 9}} \right)$$
3
IIT-JEE 1994
Subjective
Through the vertex $$O$$ of parabola $${y^2} = 4x$$, chords $$OP$$ and $$OQ$$ are drawn at right angles to one another . Show that for all positions of $$P$$, $$PQ$$ cuts the axis of the parabola at a fixed point. Also find the locus of the middle point of $$PQ$$.
Answer
$${y^2} = 2\left( {x - 4} \right)$$
4
IIT-JEE 1991
Subjective
Three normals are drawn from the point $$(c, 0)$$ to the curve $${y^2} = x.$$ Show that $$c$$ must be greater than $$1/2$$. One normal is always the $$x$$-axis. Find $$c$$ for which the other two normals are perpendicular to each other.
Answer
$$c = {3 \over 4}$$
Questions Asked from Conic Sections
On those following papers in Subjective
Number in Brackets after Paper Indicates No. of Questions