Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 20

HARD

JEE Main

IMPORTANT

Earn 100

Find the point from which the tangents to the three circles x² + y² = 1,x² + y² - 8x + 15 = 0 and x² + y²+ l0y + 24 = 0 are equal in length.

Important Questions on Circle

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 21

If

A_{i}

is the centre of the circle,

x^{2} + y^{2} + 2 g_{i} x + 5 = 0

and

t_{i}

is the length of the tangent from any point to this circle,

i = 1, 2, 3;

then show that

$(g_{2} - g_{3}) t_{1}^{2} + (g_{3} - g_{1}) t_{2}^{2} + (g_{1} - g_{2}) t_{3}^{2} = 0$

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 22

Show that if the length of the tangent from a point

P

to the circle

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

be four times the length of the tangent from it to the circle

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

then

P

lies on the circle

15 x^{2} + 15 y^{2} - 32 a x + a^{2} = 0 .

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 23

Find the equations of tangents to the circle

x^{2} + y^{2} = 25

which pass through

(7, 1)

and show that they are at right angles.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 24

Find the equation of the pair of tangents from the origin to the circle

x^{2} + y^{2} + 2 g x + 2 f y + k^{2} = 0,

and show that their intercept on the line

y = h

is

\frac{2 h k}{k^{2} - g^{2}}

times the radius of the circle.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 25

Find the equation of the chord of the circle

x^{2} + y^{2} + 6 x + 8 y + 9 = 0,

whose middle point is

(- 2, - 3)

.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 26

Find the coordinates of the middle point of the chord which the circle

$x^{2} + y^{2} + 4 x - 2 y - 3 = 0$ cuts off on the line $y = x + 2$

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 27

Find the equation to the chord of contact of the tangents drawn from an external point

(- 3, 2)

to the circle

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

.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 28

Find the coordinates of the point of intersection of tangents at the points where the line

2 x + y + 12 = 0

meets the circle

x^{2} + y^{2} - 4 x + 3 y - 1 = 0