Question

3. (1) Find the equation of a circle concentric with the circle
2 x2 +2 y2 – 6 x+8 y+1 = 0 and double of its area.​

Answer 1

Answer

Step-by-step explanation:

The given circle is:

2x²+2y²-6x+8y+1=0

i.e. x²+y²-3x+4y+½=0

Its centre is (3/2-2)² and radius= √9/4+4-½= √23/2

:Since the required circle is concentric with the given circle,

:Its centre is (3/2,-2)

If 'r1' is the radius of the required circle, then by the question,

πr1²= 2(area of given circle)

=2π(23/4) => r1²=23/2

The equation of the required circle is:

(x-3/2)²+(y+2)²= 23/2

=> x²+y²-3x+4y-21/4= 0

=> 4x²+4y²-12x+16y-21= 0

Hope this is your answer