Intermediate Second Year Mathematics Paper 2B>Chapter 1 - Circle>Exercise 1(d)>Q II

HARD

12th Andhra Pradesh Board

IMPORTANT

Earn 100

Find the slope of the polar of $(1, 3)$ with respect to the circle $x^{2} + y^{2} - 4 x - 4 y - 4 = 0$ . Also find the distance from the center to it.

Important Questions on Circle

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 1 - Circle>Exercise 1(d)>Q II

If

a x + b y + c = 0

is the polar of

(1, 1)

with respect to the circle

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

and

H . C . F . of a, b, c

is equal to one then find

a^{2} + b^{2} + c^{2}

.

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 1 - Circle>Exercise 1(d)>Q III

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

x + 4 y - 14 = 0

meets the circle

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

.

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 1 - Circle>Exercise 1(d)>Q III

If the polar of the points on the circle

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

with respect to the circle

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

touches the circle

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

then prove that

a, b, c

are in Geometrical progression.

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 1 - Circle>Exercise 1(d)>Q III

Tangents are drawn to the circle

x^{2} + y^{2} = 16 from the point P (3, 5)

. Find the value of

k

, if the area of the triangle is formed by these tangents and the chord of contact of

P

is

\frac{k \sqrt{2}}{17}

sq. units

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 1 - Circle>Exercise 1(d)>Q III

Find the locus of the point whose polars with respect to the circles

x^{2} + y^{2} - 4 x - 4 y - 8 = 0

and

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

are mutually perpendicular.

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 1 - Circle>Exercise 1(d)>Q III

Find the locus of the foot of the perpendicular drawn from the origin to any chord of the circle

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

which subtends a right angle at the origin.

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 1 - Circle>Exercise 1(e)>Q I

Discuss the relative position of the following pairs of circles

x^{2} + y^{2} - 4 x - 6 y - 12 = 0, x^{2} + y^{2} + 6 x + 18 y + 26 = 0

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 1 - Circle>Exercise 1(e)>Q I

Discuss the relative position of the following pairs of circles

x^{2} + y^{2} + 6 x + 6 y + 14 = 0, x^{2} + y^{2} - 2 x - 4 y - 4 = 0