1

IIT-JEE 1996

Subjective

+3

-0

Points $$A, B$$ and $$C$$ lie on the parabola $${y^2} = 4ax$$. The tangents to the parabola at $$A, B$$ and $$C$$, taken in pairs, intersect at points $$P, Q$$ and $$R$$. Determine the ratio of the areas of the triangles $$ABC$$ and $$PQR$$.

2

IIT-JEE 1996

Subjective

+2

-0

From a point $$A$$ common tangents are drawn to the circle $${x^2} + {y^2} = {a^2}/2$$ and parabola $${y^2} = 4ax$$. Find the area of the quadrilateral formed by the common tangents, the chord of contact of the circle and the chord of contact of the parabola.

3

IIT-JEE 1995

Subjective

+5

-0

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.

4

IIT-JEE 1995

Subjective

+5

-0

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 $${\left( {P{F_1} - P{F_2}} \right)^2} = 4{a^2}\left( {1 - {{{b^2}} \over {{d^2}}}} \right)$$.

Questions Asked from Conic Sections (Subjective)

Number in Brackets after Paper Indicates No. of Questions

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Some Basic Concepts of Chemistry
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