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If the two circles 2x^2+2y^2-3x+6y+k=0 a...

If the two circles `2x^2+2y^2-3x+6y+k=0` and `x^2+y^2-4x+10 y+16=0` cut orthogonally, then find the value of `k` .

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To find the value of \( k \) such that the two circles cut orthogonally, we will follow these steps: ### Step 1: Rewrite the equations of the circles The first circle is given by: \[ 2x^2 + 2y^2 - 3x + 6y + k = 0 \] We can simplify this by dividing the entire equation by 2: ...
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