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AP EAMCET202018 Sep 2020Evening ShiftMathematicsEllipseActual

The equation of the ellipse with its focus at ((6,2) ) centre at ((1,2) ) and which passes through the point ((4,6) ) is

Options

  1. A( (x-1)^2 25 + (y-2)^2 16 =1 )
  2. B( (x-1)^2 25 + (y-2)^2 20 =1 )
  3. C( (x-1)^2 45 + (y-1)^2 16 =1 )
  4. D( (x-1)^2 45 + (y-2)^2 20 =1 )

Correct answer

D. ( (x-1)^2 45 + (y-2)^2 20 =1 )

Step-by-step solution

Given, Focus ( S =(6,2) ) Centre ( C =(1,2)=(h, k) ) say Point ( P =(4,6) ) Required Equation of ellipse is ( (x-1)^2 a^2 + (y-2)^2 b^2 =1 ) ...(i) Since, Eq. (i) passes through ( P (4,6) ) ( aligned (4-1)^2 a^2 + (6-2)^2 b^2 & =1 9 a^2 + 16 b^2 & =1 (ii) aligned ) Since, Focus (=(6,2) ) ( aligned (h+a e, k) & =(6,2) h+a e & =6, k & =2 1+a e & =6 a e & =5 a^2 e^2 & =25 b^2 & =a^2 (1-e^2 ) b^2 & =a^2-a^2 e^2 b^2 & =a^2-25 a^2 & =b^2+25 (iii) aligned ) Put (a^2 ) value in Eq. (ii), ( aligned 9 b^2+25 + 16 b^2 & =1 9

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