The values of lambda,for which the point (lam | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The point $(\lambda, \lambda-2)$ lies inside the ellipse $4x^2+9y^2=36$. Substituting the point into the ellipse equation: $4\lambda^2 + 9(\lambda

Vedclass · Accepted Answer

$0 < \lambda < 1$

Vedclass · Answer

(A) The point $(\lambda, \lambda-2)$ lies inside the ellipse $4x^2+9y^2=36$. Substituting the point into the ellipse equation: $4\lambda^2 + 9(\lambda-2)^2 $4\lambda^2 + 9(\lambda^2 - 4\lambda + 4) $4\lambda^2 + 9\lambda^2 - 36\lambda + 36 $13\lambda^2 - 36\lambda $\lambda(13\lambda - 36) Thus,$0 The point $(\lambda, \lambda-2)$ lies outside the parabola $y^2=x$. Substituting the point into the parabola condition $y^2 - x > 0$: $(\lambda-2)^2 - \lambda > 0$ $\lambda^2 - 4\lambda + 4 - \lambda > 0$ $\lambda^2 - 5\lambda + 4 > 0$ $(\lambda-4)(\lambda-1) > 0$ Thus,$\lambda \in (-\infty, 1) \cup (4, \infty)$ (ii). Taking the intersection of $(i)$ and (ii): $0 4)$. Since $\frac{36}{13} \approx 2.76$,the intersection is $0 < \lambda < 1$.

The values of $\lambda$,for which the point $(\lambda, \lambda-2)$ lies inside the ellipse $4x^2+9y^2=36$ and outside the parabola $y^2=x$,satisfy:

Similar Questions

Find the locus of a point which moves such that its distance from the point $(0, 0)$ is twice its distance from the $y$-axis.

The locus of the middle point of the intercept of the tangents drawn to the ellipse $x^2 + 2y^2 = 2$ between the coordinate axes is:

If the tangent at the point $(1,2)$ on the ellipse $3x^2+4y^2=19$ is also a tangent to the parabola $y^2-kx=0$,then $k=$

The equation of a common tangent to the parabola $y^2 = 4x$ and the hyperbola $xy = 2$ is

Let $P$ be the point of intersection of the common tangents to the parabola $y^2 = 12x$ and the hyperbola $8x^2 - y^2 = 8$. If $S$ and $S'$ denote the foci of the hyperbola where $S$ lies on the positive $x$-axis,then $P$ divides $SS'$ in the ratio:

Vedclass Test Series

Exam Paper Generator

Online Exam Module