Find equation of a diameter of the circle is given by x2- y2-12x-4y-6 -0 is given by -

X2+ y2 12x+4y+6 =0Completing the square in x and y,we get,(x2 12x+36)+(y2+4y+4)+6 =36+4(x2 12x+36)+(y2+4y+4) =40 6(x 6)2+(y+2)2 =34Now, nbsp;Compare this equ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Director Circle

Find equation...

Question

Find equation of a diameter of the circle is given by x²+ y²-12x+4y+6 =0 is given by ?

Open in App

Solution

x²+ y²-12x+4y+6 =0
Completing the square in x and y,we get,
(x²-12x+36)+(y²+4y+4)+6 =36+4
(x²- 12x+36)+(y²+4y+4) =40-6
(x-6)²+(y+2)² =34
Now,
Compare this equation to the general equation of a circle centered at (h,k) with a radius R.
(x-h)²+(y-k)² =R²
Centre = (h, k)=(6,-2)
Radius, R = âˆš34
and
Diameter = 2R=2âˆš34

Suggest Corrections

Similar questions

Q. Equation of the diameter of the circle

x^{2} + y^{2} - 12 x + 4 y + 3 = 0

is given by:

Q. One of the diameters, of the circle

x^{2} + y^{2} - 12 x + 4 y + 6 = 0

is given by

Q. Find the center and radius of the circle whose equation is given by

x^{2} + y^{2} + 4 y = 0

Q. Find the angle between the circle given by the equations

x^{2} + y^{2} - 12 x - 6 y + 41 = 0, x^{2} + y^{2} + 4 x + 6 y - 59 = 0

C_{1} = x^{2} + y^{2} - 4 x - 8 y - 5 = 0

and

C_{2} = x^{2} + y^{2} - 12 x - 2 y + 12 = 0

are the equations of two given circles. The equation of the circle on the common chord

P Q

as diameter is:

Join BYJU'S Learning Program

Find equation of a diameter of the circle is given by x2+ y2-12x+4y+6 =0 is given by ?

Find equation of a diameter of the circle is given by x²+ y²-12x+4y+6 =0 is given by ?