The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XVIII>Q 19

HARD

JEE Advanced

IMPORTANT

Earn 100

Find the equation of a circle of radius $r$ , which touches the axis of $y$ at a point at distance $h$ from the origin, the center of the circle being in the positive quadrant. Also, prove that the equation of the other tangent which passes through the origin is, $(r^{2} - h^{2}) x + 2 r h y = 0$ .

Important Questions on The Circle

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XVIII>Q 20

Find the equation of the circle whose center is at the point

(α, β)

and which passes through the origin, and prove that the equation of the tangent at the origin is,

αx + βy = 0

.

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XVIII>Q 21

Two circles are drawn through the points $(a, 5 a)$ and $(4 a, a)$ to touch the axis of $y$ , where $a > 0$ . Prove that they intersect at an angle $\tan^{- 1} (\frac{40}{9})$ .

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XVIII>Q 22

A circle passes through the points

(- 1, 1), (0, 6)

and

(5, 5)

. Find the points on this circle the tangents at which are parallel to the straight line joining the origin to its center.

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XIX>Q 11

Tangents are drawn to the circle

x^{2} + y^{2} = 12

at the points where it is met by the circle

x^{2} + y^{2} - 5 x + 3 y - 2 = 0

. Find the point of intersection of these tangents.

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XIX>Q 14

Find the condition that the chord of contact of tangents from the point

(x^{'}, y^{'})

, to the circle

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

, should subtend a right angle at the center.

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XIX>Q 17

Tangents are drawn from the point

(h, k)

to the circle

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

. Prove that the area of the triangle formed by them, and the straight line joining their points of contact is

\frac{a {(h^{2} + k^{2} - a^{2})}^{\frac{3}{2}}}{h^{2} + k^{2}}

. Find the lengths of the tangents drawn.

EASY

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XIX>Q 18

Find the length of tangent to the circle

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

from the point

(- 2, 3)

.

EASY

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 6 - The Circle>EXAMPLES XIX>Q 19

Find the length of the tangents drawn to the circle

3 x^{2} + 3 y^{2} - 7 x - 6 y = 12

from the point

(6, - 7)

.