Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 43

HARD

JEE Main/Advance

IMPORTANT

Earn 100

Equation of a circle passing through $(2, 8)$ and touching the lines $4 x - 3 y - 24 = 0$ and $4 x + 3 y - 42 = 0$ and having $x$ -coordinate of the centre less than or equal to $8$ is

50% studentsanswered this correctly

Important Questions on Conic Section

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 44

A square is inscribed in the circle

x^{2} + y^{2} - 2 x + 4 y + 3 = 0

. Its sides are parallel to the co-ordinate axes, then one vertex of the square is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 45

From the origin

O

tangents

O P

and

O Q

are drawn to the circle

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

. Then the circumcentre of the triangle

O P Q

lies at

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 46

Area of a circle in which a chord of length

\sqrt{2}

makes an angle

\frac{π}{2}

at the centre is

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 47

If

3 x + b_{1} y + 5 = 0

and

4 x + b_{2} y + 10 = 0

cut the

x

-axis and

y

-axis in four concyclic points, then the value of

b_{1} b_{2}

is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 48

The image of the centre of a circle

(x - 2)^{2} + (y - 1)^{2} = 9

w.r.t. the line

y = x

moves

\sqrt{2}

units along

(N - E)

direction then the co-ordinates of the centre in the new position is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 49

The equation of the circle whose radius is

5

and which touches the circle

x^{2} + y^{2} - 2 x - 4 y - 20 = 0

externally at the point

(5, 5)

, is

x^{2} + y^{2} - 18 x + λ y + μ = 0

then

(λ + μ)

is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 50

A circle has radius

3

units and its centre lies on the line

y = x - 1

. If the circle passes through point

(7, 3)

and has centre at point

(h, k)

then

h^{k}

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 51

If the length of the tangent from any point on the circle

(x - 3)^{2} + (y + 2)^{2} = 5 r^{2}

to the circle

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

is

16

units, then the area between the two circles is

λ π

sq. units then

λ

is equal to