Solve fast no link tomorrow exam: 8 The line 2x-y+6=0 meets the circle x2+y2+10x+9=0 at A and B - Maths -

Question

Solve fast no link tomorrow exam:

8 The line 2x-y+6=0 meets the circle
x2+y2+10x+9=0 at A and B Find the equation of
circle on AB as diameter

Lovina Kansal · Accepted Answer

Dear student
We have, Equation of line, 2x-y+6=0⇒y=2x+6    
(1)Equation of curve,x2+y2+10x+9=0    
(2)⇒x2+(2x+6)2+10x+9=0   [using 1]⇒x2+4x2+36+24x+10x+9=0⇒5x2+34x+45=0⇒x=-34±342-4(5)(45)2(5)⇒x=-34±1156-90010⇒x=-34±1610⇒x=-5 or x=-95When x=-5 then y=2(-5)+6=-4When x=-95 then y=2-95+6=125So, the chordinates of end points of A is -5,-4 and B is -95,125The distance AB is the length of the diameter ABAB=-95+52+125+42=25625+102425=1655 unitsRadius of the circle is 12×1655=855unitsMid-point of AB is the center of the circle=-5-952,-4+1252=-175,-45Thus the equation of the circle is x+1752+y+452=8552⇒x2+28925+34x5+y2+1625+8y5=645⇒x2+y2+34x5+8y5-35=0⇒5x2+5y2+34x+8y-3=0which is the required equation of the circle
Regards

Solve fast no link tomorrow exam: 8. The line 2x-y+6=0 meets the circle x2+y2+10x+9=0 at A and B. Find the equation of circle on AB as diameter.

Solve fast no link tomorrow exam:

8. The line 2x-y+6=0 meets the circle x²+y²+10x+9=0 at A and B. Find the equation of circle on AB as diameter.