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NTA Abhyas JEE Main2020MathematicsHyperbolaPractice

Let the variable line y = k x + h is tangent to the hyperbola x 2 4 - y 2 9 = 1 . If the locus of P h , k is a conic, then which of the following statement is false about this conic?

Options

  1. AVertices of conic lies on y-axis
  2. BThe eccentricity of conic is greater than the eccentricity of given hyperbola.
  3. CThe centre of conic is at the origin
  4. DThe conic is an ellipse

Correct answer

D. The conic is an ellipse

Step-by-step solution

Equation of the tangent y = k x + h is compared with y = m x ± 4 m 2 - 9 ⇒ 1 = m k = ± 4 m 2 - 9 h i.e. m = k and h = 4 m 2 - 9 ⇒ h = 4 k 2 - 9 ⇒ 4 y 2 - x 2 = 9 ⇒ y 2 3 2 2 - x 2 3 2 = 1 ⇒ 3 2 = 3 2 2 e 2 - 1 ⇒ e 2 = 5 ⇒ e = 5 > 1 Hence, the conic is not an ellipse

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