0

Guest

Courses New

A circle passes through (2,1) and x+2y=1 is a tangent to a circle at (3,-1) find its equation? Please provide with the answer fast!

A circle passes through (2,1) and x+2y=1 is a tangent to a circle at (3,-1) find its equation? Please provide with the answer fast!

Grade:12th pass

1 Answers

Arif Hossain
askIITians Faculty 52 Points
7 years ago
Since x+2y=1 tangent, a diameter will be perpendicular to the line and pass thru (3,-1). The slope of that line is +2, the negative inverse of the line x+2y=1
The eqn of the line thru the center of the circle and thru (3,-1) is:
y= 2x-7
Now, the center of the circle is on that line and equidistant from (3,-1) and (2,1).
so,

sqrt[(x-3)^2 + (y+1)^2] = sqrt[(x-2)^2 + (y-1)^2]

or, x=2y+5/2
Therefore co-ordinate of center is (2y+5/2,y) it's on the line y = 2x-7
so, y=2(2y+5/2)-7
or,y=2/3
The center is (23/6,2/3)
we know the center and poin on circumference of circle so we easily get the equation

Think You Can Provide A Better Answer ?

Other Related Questions on Analytical Geometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More