Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 41

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If a parabola touches the lines $y = x$ and $y = - x$ at $P (3, 3)$ and $Q (2, - 2)$ respectively, then

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Important Questions on Parabola

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 42

Let

A, B

and

C

be three distinct points on

y^{2} = 8 x

such that normals at these points are concurrent at

P

. The slope of

A B

is

2

and abscissa of centroid of

△ A B C

is

\frac{4}{3}

. Which of the following is (are) correct?

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Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 43

Let

P

and

Q

be distinct points on the parabola

y^{2} = 2 x

such that a circle with

P Q

as diameter passes through the vertex

O

of the parabola. If

P

lies in the first quadrant and the area of the triangle

Δ O P Q

is

3 \sqrt{2}

sq. units, then which of the following is (are) the coordinates of

P

?

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Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 46

The focal distance of a point on the parabola

y^{2} = 16 x

whose ordinate is twice the abscissa is (except the vertex of parabola)

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Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 47

The radius of circle which passes through the focus of the parabola

x^{2} = 4 y &

touches it at the point

(6, 9)

is

a \sqrt{10},

then value of

' a'

is

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Mathematics Crash Course JEE Advanced>Chapter 9 - Parabola>Exercise 1>Q 48

A line is a common tangent to the circle

{(x - 3)}^{2} + y^{2} = 9

and the parabola

y^{2} = 4 x

. If the two points of contact

(a, b)

and

(c, d)

are distinct and lie in the first quadrant, then

2 (a + c)

is equal to ___ .