Let the variable line y=kx+h is tangent to the hyperbola (x^2)/4-(y^2)/9=1. If the locus of Ph,k is a conic, then which of the following statement is…

Question

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

MARKS Content Team · Accepted Answer

Correct answer: (D) The conic is an ellipse. Equation of the tangent y=kx+h is compared with y=mx±√(4m^2-9) ⇒1=m/k=(±√(4m^2-9))/h i.e. m=k and h=√(4m^2-9) ⇒h=√(4k^2-9) ⇒4y^2-x^2=9 ⇒(y^2)/(3^22)-(x^2)/(3^2)=1 ⇒3^2=3^22e^2-1 ⇒e^2=5⇒e=√5>1 Hence, the conic is not an ellipse

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

Solution

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Let the variable line y=kx+h is tangent to the hyperbola x24-y29=1. If the locus of Ph,k is a conic, then which of the following statement is false about this conic?

Solution

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