The sides of a rectangle are given by x- a and y- b- The equation of the circle passing through the vertices of the rectangle is

The correct option is B x ^ 2 + y ^ 2 = a ^ 2 + b ^ 2 From the #160; figure it is clear that the center of the circle is at origin and its radius r= ...

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Standard XII

Mathematics

f(x) Transforms to f(-x)

The sides of ...

Question

The sides of a rectangle are given by $x = \pm a$ and $y = \pm b$ . The equation of the circle passing through the vertices of the rectangle is

x^{2} + y^{2} = a^{2}

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x^{2} + y^{2} = a^{2} + b^{2}

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x^{2} + y^{2} = a^{2} - b^{2}

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{(x - a)}^{2} + {(y - b)}^{2} = a^{2} + b^{2}

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Solution

The correct option is B $x^{2} + y^{2} = a^{2} + b^{2}$
From the figure it is clear that the center of the circle is at origin and its radius

$r = \sqrt{a^{2} + b^{2}}$

Equation of the circle:-

$x^{2} + y^{2} = r^{2}$

$⟹ x^{2} + y^{2} = a^{2} + b^{2}$

Hence, answer is option-(B).

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Similar questions

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is:

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The sides of a rectangle are given by x=±a and y=±b. The equation of the circle passing through the vertices of the rectangle is

The correct option is B x2+y2=a2+b2From the figure it is clear that the center of the circle is at origin and its radiusr=√a2+b2Equation of the circle:-x2+y2=r2⟹x2+y2=a2+b2Hence, answer is option-(B).

The sides of a rectangle are given by $x = \pm a$ and $y = \pm b$ . The equation of the circle passing through the vertices of the rectangle is

The correct option is B $x^{2} + y^{2} = a^{2} + b^{2}$
From the figure it is clear that the center of the circle is at origin and its radius

$r = \sqrt{a^{2} + b^{2}}$

Equation of the circle:-

$x^{2} + y^{2} = r^{2}$

$⟹ x^{2} + y^{2} = a^{2} + b^{2}$

Hence, answer is option-(B).