Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 41

HARD

JEE Main/Advance

IMPORTANT

Earn 100

Consider two circles $C_{1} : x^{2} + y^{2} - 1 = 0$ and $C_{2} : x^{2} + y^{2} - 2 = 0$ . Let $A (1, 0)$ be a fixed point on the circle $C_{1}$ and $B$ be any variable point on the circle $C_{2}$ . The line $B A$ meets the curve $C_{2}$ again at $C$ . Which of the following is/are correct?

50% studentsanswered this correctly

Important Questions on Circle

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 42

One of the diameter of the circle circumscribing the rectangle

A B C D

is

x - y - 1 = 0

. If two vertices of rectangle are the points

(- 2, 5)

and

(6, 5)

respectively, then which of the following hold

(s)

good?

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 43

Three concentric circles of which the biggest is

x^{2} + y^{2} = 1,

have their radii in A.P. If the line

y = x + 1

cuts all the circles in real and distinct points. The permissible values of common difference of

A . P .

is/are

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 44

If

4 l^{2} - 5 m^{2} + 6 l + 1 = 0

and the line

l x + m y + 1 = 0

touches

a

definite circle, then which of the following İs/are true?

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 45

If the circle

C_{1} : x^{2} + y^{2} = 16

intersects another circle

C_{2}

of radius

5

in such a manner that the common chord is of maximum length and has a slope equal to

\frac{3}{4},

then the coordinates of the centre of

C_{2}

are

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 46

For the circles

x^{2} + y^{2} - 10 x + 16 y + 89 - r^{2} = 0

and

x^{2} + y^{2} + 6 x - 14 y + 42 = 0

which of the following is/are trüe?

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 47

Which of the following statement

(s)

is/are correct with respect to the circles

S_{1} \equiv x^{2} + y^{2} - 4 = 0

and

S_{2} \equiv x^{2} + y^{2} - 2 x - 4 y + 4 = 0 ?

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 48

Two circles, each of radius

5

units, touch each other at

(1, 2) .

If the equation of their common tangent is

4 x + 3 y = 10 .

The equations of the circles are

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 49

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

and

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

are two equal circles touching each other. Find the equation of circle (or circles) of the same radius touching both the circles.