Find the centre and radius of the circles.
$x^{2} + y^{2} - 4 x - 8 y - 5 = 0$

Question

Find the centre and radius of the circle x-2-y-2-4x - 8y -45-0-2-6- sqrt -63-2-4- sqrt -65-2-4- sqrt -66-None

Toppr Admin · Accepted Answer

Given circle equation-xA0- x2-y2-x2212-4x-x2212-8y-x2212-45-0here2g-x2212-4-x2234-g-x2212-2and2f-x2212-8-x2234-f-x2212-4-x2234-centre-x2212-g-x2212-f-2-4-radius-x221A-g2-f2-x2212-c-x221A-22-42-x2212-x2212-45-x221A-4-16-45-x221A-65unit

Find the centre and radius of the circle $x^{2} + y^{2} - 4 x - 8 y - 45 = 0$ .
$(2, 6), \sqrt{63}$
$(2, 4), \sqrt{65}$
$(2, - 4), \sqrt{66}$
None

Given circle equation $x^{2} + y^{2} - 4 x - 8 y - 45 = 0 h e r e 2 g = - 4 ∴ g = - 2 a n d 2 f = - 8 ∴ f = - 4 ∴ c e n t r e (- g, - f) = (2, 4) r a d i u s = \sqrt{g^{2} + f^{2} - c} = \sqrt{2^{2} + 4^{2} - (- 45)} = \sqrt{4 + 16 + 45} = \sqrt{65} u n i t$

Find the centre and radius of the circle x2+y2−4x−8y−45=0.(2,6),√63(2,4),√65(2,−4),√66None

Given circle equation x2+y2−4x−8y−45=0here2g=−4∴g=−2and2f=−8∴f=−4∴centre(−g,−f)=(2,4)radius=√g2+f2−c=√22+42−(−45)=√4+16+45=√65unit

Find the centre and radius of the circle $x^{2} + y^{2} - 4 x - 8 y - 45 = 0$ .
$(2, 6), \sqrt{63}$
$(2, 4), \sqrt{65}$
$(2, - 4), \sqrt{66}$
None

Given circle equation $x^{2} + y^{2} - 4 x - 8 y - 45 = 0 h e r e 2 g = - 4 ∴ g = - 2 a n d 2 f = - 8 ∴ f = - 4 ∴ c e n t r e (- g, - f) = (2, 4) r a d i u s = \sqrt{g^{2} + f^{2} - c} = \sqrt{2^{2} + 4^{2} - (- 45)} = \sqrt{4 + 16 + 45} = \sqrt{65} u n i t$