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Standard XII

Mathematics

Obtaining Centre and Radius of a Circle from General Equation of a Circle

If a circle ...

Question

If a circle $x^{2} + y^{2} = 225$ intersects are rectangular hyperbola at four points $(12, 9), (9, 12), (15, 0)$ and $(0, 15)$ , then find the centre of the recatangular hyperbola.

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Solution

REF.Image.
Given
$x^{2} + y^{2} = 225$
we know
let $c_{2} (h, k)$
$\frac{A + B + C + D}{4} = \frac{c_{1} + c_{2}}{2}$
$\frac{12 + 9 + 15 + 0}{4} = \frac{0 + h}{2}$
$\Rightarrow h = 18$
$\frac{9 + 12 + 0 + 15}{4} = \frac{0 + k}{2}$
$\Rightarrow k = 18$
centre of rectangular Hyper is (18,18)

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If a circle x2+y2=225 intersects are rectangular hyperbola at four points (12,9),(9,12),(15,0) and (0,15), then find the centre of the recatangular hyperbola.

REF.Image.Givenx2+y2=225we knowlet c2(h,k)A+B+C+D4=c1+c2212+9+15+04=0+h2⇒h=189+12+0+154=0+k2⇒k=18centre of rectangular Hyper is (18,18)

If a circle $x^{2} + y^{2} = 225$ intersects are rectangular hyperbola at four points $(12, 9), (9, 12), (15, 0)$ and $(0, 15)$ , then find the centre of the recatangular hyperbola.

REF.Image.
Given
$x^{2} + y^{2} = 225$
we know
let $c_{2} (h, k)$
$\frac{A + B + C + D}{4} = \frac{c_{1} + c_{2}}{2}$
$\frac{12 + 9 + 15 + 0}{4} = \frac{0 + h}{2}$
$\Rightarrow h = 18$
$\frac{9 + 12 + 0 + 15}{4} = \frac{0 + k}{2}$
$\Rightarrow k = 18$
centre of rectangular Hyper is (18,18)