﻿ The line (x – 2) cos θ + (y – 2) sin θ = 1 touches a circle for all values of θ. Find the circle. : Kaysons Education

# The Line (x – 2) Cos θ + (y – 2) Sin θ = 1 Touches A Circle For All Values Of θ. Find The Circle.

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## Question

### Solution

Correct option is

x2 + y2 – 4x – 4y + 7 = 0

Given line is

squaring and adding (1) and (2), then (x – 2)2 + (y – 2)2 = cos2θ + sin2θ

⇒                     (x – 2)2 + (y – 2)2 = 1

or                     x2 + y2 – 4x – 4y + 7 = 0

Testing

#### SIMILAR QUESTIONS

Q1

Find the points of intersection of the line 2x + 3y = 18 and the circle x2 +y2 = 25.

Q2

Find the length of the intercept on the straight line 4x – 3y – 10 = 0 by the circle x2 + y2 – 2x + 4y – 20 = 0.

Q3

Find the co-ordinates of the middle point of the chord which the circlex2 + y2 + 4x – 2y – 3 = 0 cuts off the line x – y + 2 = 0.

Q4

For what value of λ will the line = 2x + λ be a tangent to the circle x2 +y2 = 5?

Q5

Find the equation of tangent to the circle x2 + y2 – 2ax = 0 at the point

Q6

Find the equation of the tangents to the circle x2 + y2 = 9, which  Are parallel to the line 3x + 4y – 5 = 0

Q7

Find the equation of the tangents to the circle x2 + y2 = 9, which

Are perpendicular to the line 2x + 3y + 7 = 0.

Q8

Find the equation of the tangents to the circle x2 + y2 = 9, which make an angle of 60o with the x-axis.

Q9

Show that the line 3x – 4y = 1 touches the circle x2 + y2 – 2x + 4y + 1 = 0. Find the co-ordinates of the point of contact.

Q10

Find the equation of the normal to the circle

x2 + y2 – 5x + 2y – 48 = 0 at the point (5, 6).