Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 34

HARD

JEE Advanced

IMPORTANT

Earn 100

Circle drawn having its diameter equal to focal distance of any point lying on the parabola $x^{2} - 4 x + 6 y + 10 = 0,$ will touch a fixed line whose equation is

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Important Questions on Parabola

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 35

An equilateral

Δ S A B

is inscribed in the parabola

y^{2} = 4 a x

having its focus at

S .

If chord

A B

lies towards the left of

S,

then side length of this triangle is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 36

Normals

A O, A A_{1}, A A_{2}

are drawn to the parabola

y^{2} = 8 x

from the point

A (h, 0) .

If

Δ O A_{1} A_{2}

is equilateral, then the possible values of

h

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 37

The locus of centre of a circle that passes through

P (a, b)

and touch the line

y = m x + c

(it is given that,

b \neq m a + c

) is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 38

The parabola

y^{2} = 4 x

and the circle

{(x - 6)}^{2} + y^{2} = r^{2}

will have no common tangent, if

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 39

Parabola

y^{2} = 4 x

and the circle having its centre at

(6, 5)

intersect at right angle. The possible point of intersection of these curves can be

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 40

y = 2 x + c, c

being a variable, is a chord of the parabola

y^{2} = 4 x,

meeting the parabola at

A

and

B .

Locus of point dividing the segment

A B

internally in the ratio

1 : 1,

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 41

Radius of the circle that passes through origin and touches the parabola

y^{2} = 4 a x

at the point

(a, 2 a)

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 42

A line

L

passing through the focus of the parabola

{(y - 2)}^{2} = 4 (x + 1)

and intersects the parabola in two distinct points. If

m

is the slope of the line

L,

then

m

can take values in the interval