﻿ If two circles which pass through the points (0, a) and (0, –a) cut each other orthogonally and touch the straight line  y = mx + c, then : Kaysons Education

# If Two Circles Which Pass Through The Points (0, a) And (0, –a) Cut Each Other Orthogonally And Touch The Straight Line  Y = mx + c, Then

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## Question

### Solution

Correct option is

c2 = a2 (2 + m2)

Equation of a family of circles through (0 , a) and (0, –a) is x2 + y2 + 2λax – a2 = 0. If two members are for λ = λ1 and λ = λ2 then since they intersect orthogonally 1λ2a2 = –2a2 ⇒ λ1λ2 = –1

Since the two circles touch the line y = mx + c

#### SIMILAR QUESTIONS

Q1

An equation of the circle through (1, 1) and the points of intersection ofx2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0 is

Q2

The abscissae of two points A and B are the roots of the equation x2 + 2ax – b2 = 0, and their ordinates are the roots of the equation x2 + 2px –q2 = 0. The radius of the circle with AB as diameter is

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Q5

If the two circles x2 + y2 + 2gx + 2fy = 0 and x2 + y2 + 2g1x + 2f1y = 0 touch each other, then

Q6

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Q7

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