EASY

JEE Advanced

IMPORTANT

Earn 100

If the points on the parabola $y^{2} = 18 x$ , when ordinate is equal to three times the abscissa are $(0, 0)$ and $(a, b)$ , then find $a + b$ .

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Important Questions on Conic Sections. The Parabola

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 8 - Conic Sections. The Parabola>EXAMPLES XXV>Q 10

Prove that the equation of the parabola, whose vertex and focus are on the

x

axis at the distance of

a

and

a^{'}

from the origin respectively, is

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

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 8 - Conic Sections. The Parabola>EXAMPLES XXV>Q 11

In the parabola

y^{2} = 6 x

, the equation of the chord through the vertex and the negative end of the latus rectum is given as

a x + b y + c = 0

. Find

a b + c

EASY

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 8 - Conic Sections. The Parabola>EXAMPLES XXV>Q 11

For the parabola

y^{2} = 6 x

, the equation of any chord with slope

m

and through a point on the curve lying in the first quadrant whose abscissa is

24

y - a = m (x - b)

. Find

a + b

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 8 - Conic Sections. The Parabola>EXAMPLES XXV>Q 12

The equation

y^{2} + 2 A x + 2 B y + C = 0

represents a parabola, whose axis is parallel to the axis of

x

, the equation to its latus rectum is

x = \frac{B^{p} - A^{q} - C}{2 A}

. Find

(p + q)

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 8 - Conic Sections. The Parabola>EXAMPLES XXV>Q 13

Prove that the locus of the middle points of all chords of the parabola

y^{2} = 4 a x

which are drawn through the vertex is the parabola

y^{2} = 2 a x

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 8 - Conic Sections. The Parabola>EXAMPLES XXV>Q 14

Prove that the locus of the centre of a circle, which intercepts a chord of given length

2 a

on the axis of

x

and passes through a given point on the axis of

y

distant

b

from the origin, is the curve

x^{2} - 2 y b + b^{2} = a^{2}

. Trace this parabola.

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 8 - Conic Sections. The Parabola>EXAMPLES XXV>Q 15

P Q

is a double ordinate of a parabola. The locus of its points of trisection is

k y^{2} = 4 a x

. Find

k

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 8 - Conic Sections. The Parabola>EXAMPLES XXV>Q 16

Prove that the locus of a point, which moves so that its distance from a fixed line not passing through center of circle is equal to the length of the tangent drawn from it to a given circle, is a parabola. Find the position of the focus and directrix.

If the points on the parabola y2=18x, when ordinate is equal to three times the abscissa are 0,0 and a,b, then find a+b.

Important Questions on Conic Sections. The Parabola

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If the points on the parabola $y^{2} = 18 x$ , when ordinate is equal to three times the abscissa are $(0, 0)$ and $(a, b)$ , then find $a + b$ .