For what positive value(s) of K will the graph of the equation $2 x + y = K$ be tangent to the graph of the equation $x^{2} + y^{2} = 45$ ?

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Solution

The correct option is C 15
The radius of circle is $\sqrt{45} = 3 \sqrt{5}$ , center of circle is $(0, 0)$
For the equation to be tangent to circle , the distance from center of circle to given line must be equal to radius of circle
So we get $k / \sqrt{5} = 3 \sqrt{5}$ , which gives $k = 15$

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x = 6

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

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y = x^{2} - 2 x + 7

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