MEDIUM

JEE Advanced

IMPORTANT

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From the external point $P$ , tangents are drawn to the parabola; find the equation to the locus of $P$ , when these tangents make angles $θ_{1}$ and, $θ_{2}$ with the axis such that, $\tan^{2} θ_{1} + \tan^{2} θ_{2}$ is a constant $(= λ)$ .

Important Questions on The Parabola (Continued)

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 6

From an external point

P

, tangents are drawn to the parabola,

y^{2} = 4 a x

; find the equation of the locus of

P

when these tangents make angles

θ_{1}

and

θ_{2}

with the axis, such that

\cos θ_{1} \cos θ_{2}

is a constant

(= μ) .

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 7

Two tangents to a parabola meet at an angle

45 °;

prove that the locus of their point of intersection is the curve

y^{2} - 4 a x = {(x + a)}^{2}

. If they meet at an angle

60 °

; prove that the locus is,

y^{2} - 3 x^{2} - 10 a x - 3 a^{2} = 0

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 8

A pair of tangents are drawn to a parabola and are equally inclined to a straight line whose inclination to the axis is

α

; prove that the locus of their point of intersection is the straight line

y = (x - a) \tan 2 α .

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 9

Prove that the locus of the point of intersection of two tangents which intercepts a given distance,

4 c

on the tangent at the vertex is an equal parabola.

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 10

Show that the locus of the point of intersection of two tangents with which the tangent at the vertex form triangle of constant area

c^{2}

is the curve

x^{2} (y^{2} - 4 a x) = 4 c^{4} .

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 12

Two tangents to a parabola intercept on a fixed tangent segments whose product is constant; prove that the locus of their point of intersection is straight line.

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 16

Two equal parabolas,

A

and

B

, have the same vertex and axis but their concavities turned in opposite directions. Prove that the locus of poles with respect to

B

of tangents from

A

is the parabola

A

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 19

Find the locus of the middle points of chords of the parabola which passes through the focus.

From the external point P, tangents are drawn to the parabola; find the equation to the locus of P, when these tangents make angles θ1 and, θ2 with the axis such that, tan2⁡θ1+tan2⁡θ2 is a constant=λ.

Important Questions on The Parabola (Continued)

Learn and Prepare for any exam you want !

From the external point $P$ , tangents are drawn to the parabola; find the equation to the locus of $P$ , when these tangents make angles $θ_{1}$ and, $θ_{2}$ with the axis such that, $\tan^{2} θ_{1} + \tan^{2} θ_{2}$ is a constant $(= λ)$ .