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Show that the equation 3x^2-x+7=0 can ...

Show that the equation `3x^2-x+7=0` can not be satisfied by any real values of x.

Text Solution

Verified by Experts

The correct Answer is:
`(2,-3)`
Let origin be shifted at point (h,k) without rotating the coordinate axes.
Now, we replace x by `(x+h)` and y by `(y+k)` in the equation of given curve.
Then the transformed equation is
`(x+h)^2+(y+k)^2-4(x+h)+6(y+k)-7=0`
`rArrx^2+y^2+x(2h-4)+y(2k+6)+h^2+k^2-4h+6k-7=0`
Since, this equation does not contain the terms of first degree.
`therefore 2h-4=0and 2k+6=0`
`rArrh=2and k=-3`
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