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Manipal MET2011MathematicsEllipse

The equation of the ellipse whose axes are parallel to the coordinate axes having its centre at the point (2,-3) and focus at (3,-3) and one vertex at (4,-3) is

Options

  1. A(x-2)^2 4 + (y+3)^2 3 =1
  2. B(x+2)^2 3 + (y+3)^2 4 =1
  3. C(x+2)^2 4 + (y+3)^2 3 =1
  4. DNone of the above

Correct answer

A. (x-2)^2 4 + (y+3)^2 3 =1

Step-by-step solution

Let 2 a and 2 b be the major and minor axes of the ellipse. Then, its equation is (x-2)^2 a^2 + (y+3)^2 b^2 =1 ..(i) (4-2)^2+(-3+3)^2 =aa=2 ...(ii) Here, C S=a e (2-3)^2+(-3+3)^2 =a e a e=1 ...(iii) From Eqs. (ii) and (iii), we get e= 1 2 Now, b^2=a^2 (1-e^2 ) b^2=4 (1- 1 4 )=3 On substituting the values of a and b in Eq. (i) we get (x-2)^2 4 + (y+3)^2 3 =1

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