AP EAMCET · Maths · Ellipse
The point \((1,3)\) with respect to the ellipse \(4 x^2+9 y^2-16 x-54 y+61=0\) lies
- A outside the ellipse
- B on the ellipse
- C on the minor axis
- D on the major axis
Answer & Solution
Correct Answer
(D) on the major axis
Step-by-step Solution
Detailed explanation
Given, equation of ellipse is \[ 4 x^2+9 y^2-16 x-54 y+61=0 \] It can be written as, \[ \frac{(x-2)^2}{9}+\frac{(y-3)^2}{4}=1 \] Centre of ellipse \((2,3)\). vertex are \((5,3),(-1,3)\) Focus are \((2+\sqrt{5}, 3),(2-\sqrt{5}, 3)\) \(\therefore(1,3)\) lies on major axis.
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