Question

5. Find the point to which the origin should be shifted so that the
${x}^{2} + {y}^{2} - 10x + 4y - 20 = 0$
may not contain first degree terms in x and y.
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Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Let the origin be shifted to the point (h,k).

Let (x,y) and (x′,y′) are the coordinates of a point in the old and new system respectively, then x=x′+h,y=y′+k.

So, the transformed equation is

14(x′+h)2−4(x′+h)(y′+k)+11(y′+k)2−36(x′+h)+48(y′+k)+41=0⇒14x′2+28x′h+14h2−4x′y′−4x′k−4y′h−4hk+11y′2+11k2+22y′k−36x′−36h+48y′+48k+41=0⇒14x′2+11y′2+x