UPSC NDA Math Model Paper 3

Observe that the given equation is of the form F(x,y)=k, where F(x,y)=2x2+7y2 and k=20.
Therefore, to find the position of the given point (1, 2) with respect to ellipse substitute x = 1 and y = 2 in the equation of the ellipse..
Therefore,
2(1)2+7(2)2=30
But 30 > 20 therefore we have F(1, 2) > k and therefore the point (1, 2) lies outside the ellipse.