﻿ Examine if the two circles x2 + y2 – 2x – 4y = 0 and x2 + y2 – 8y – 4 = 0 touch each other externally or internally. : Kaysons Education

# Examine If The Two Circles x2 + y2 – 2x – 4y = 0 And x2 + y2 – 8y – 4 = 0 Touch Each Other Externally Or Internally.

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## Question

### Solution

Correct option is

Internally

Given circles are

x2 + y2 – 2x – 4y = 0                       …(1)

and                x2 + y2 – 8y – 4 = 0                         …(2)

let centres and radii of circles (1) and (2) are represented by C1r1 andC2r2 respectively.

Hence the two circles touch each other internally.

#### SIMILAR QUESTIONS

Q1

Find the condition that chord of contact of any external point

(hk) to the circle x2 + y2 = a2 should subtend right angle at the centre of the circle.

Q2

The chord of contact of tangents drawn from a point on the circle x2 +y2 = a2 to the circle x2 + y2 = b2 touches the circle x2 = y2 = c2. Show that abc are in GP.

Q3

Find the equation of the chord x2 + y2 – 6x + 10y – 9 = 0 which is bisected at (–2, 4).

Q4

Find the middle point of the chord intercepted on line lx + my + n = 0 by the circle x2 + y2 = a2.

Q5

Find the locus of middle points of chords of the circle x2 + y2 = a2, which subtend right angle at the point (c, 0).

Q6

Find the equations of the tangents from the point A(3, 2) to the circle x2y2 + 4x + 6y + 8 = 0 .

Q7

If two tangents are drawn from a point on the circle x2 + y2 = 50 to the circle x2 + y2 = 25 then find the angle between the tangents.

Q8

Find the equation of the diameter of the circle

x2 + y2 + 2gx + 2fy + c = 0 which corresponds to the chord ax = by + d= 0.

Q9

Find the locus of the pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.

Q10

Find the equation of the circle passing through (1, 1) and the points of intersection of the circles

x2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0.