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KCET2011MathematicsEllipse

If x +y =4 is tangent to x² 25 + y² 9 =1 , then the value of is

Options

  1. A⁻¹(3 / 7)
  2. B⁻¹( 3 / 7)
  3. C⁻¹(7 / 3)
  4. D⁻¹(3 / 7 )

Correct answer

D. ⁻¹(3 / 7 )

Step-by-step solution

Given, x +y =4 is a tangent to x² 25 + y² 9 =1 y=-x +4 cosec Here, m=- , c=4 cosec and a²=25, b²=9 Now, the condition of tangent to ellipse is c²=a² m²+b²16 cosec ² =25 ² +9 16 ² = 25 ² ² +9 16=25 ² +9 ² 9 ² +25-25 ² =16 -16 ² =-9 ² = 9 16 , =3 / 4 ² = 7 16 ² =9 / 7 = ⁻¹(3 / 7 )

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