The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 8 - Conic Sections. The Parabola>EXAMPLES XXVI>Q 9

MEDIUM

JEE Advanced

IMPORTANT

Earn 100

The equation of the tangents to the parabola $y^{2} = 9 x$ which goes through the point $(4, 10)$ are $4 y = p x + q & 4 y = r x + s$ . Find $p + q + r + s$ .

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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 XXVI>Q 10

Prove that the straight line

x + y = 1

touches the parabola

y = x - x^{2}

.

MEDIUM

JEE Advanced

IMPORTANT

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

Prove that the straight line

y = m x + c

touches the parabola

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

, if

c = m a + \frac{a}{m}

.

EASY

JEE Advanced

IMPORTANT

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

Prove that the straight line

l x + m y + n = 0

touches the parabola

y^{2} = 4 a x

, if

l n = a m^{2}

.

MEDIUM

JEE Advanced

IMPORTANT

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

Find the points on the parabola

y^{2} = 4 a x, (a > 0)

for which length of the normal is equal to twice of length of the subtangent.

MEDIUM

JEE Advanced

IMPORTANT

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

Tell the point(s) on the parabola

y^{2} = 4 a x (a > 0)

for which length of the normal is same as difference between the length of subtangent and the subnormal.

HARD

JEE Advanced

IMPORTANT

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

Find the equation to the common tangents of the parabolas

y^{2} = 4 a x

and

x^{2} = 4 b y

.

HARD

JEE Advanced

IMPORTANT

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

Find the equations to the common tangents of the circle $x^{2} + y^{2} = 4 a x$ and the parabola $y^{2} = 4 a x$ .

HARD

JEE Advanced

IMPORTANT

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

Two equal parabolas have the same vertex and their axes are at right angles. Prove that the common tangent touches each at the end of a latus rectum.