The number of integral values of lambda for | vedclass

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

Question

Here, radius $\sqrt{\left(\frac{\lambda}{2}\right)^{2}+\left(\frac{1-\lambda}{2}\right)^{2}-5 \leq 5} \quad$

$\Rightarrow 2 \lambda^{2}-2 \lambda-1

Vedclass · Accepted Answer

$16$

Vedclass · Answer

Here, radius $\sqrt{\left(\frac{\lambda}{2}ight)^{2}+\left(\frac{1-\lambda}{2}ight)^{2}-5 \leq 5} \quad$

$\Rightarrow 2 \lambda^{2}-2 \lambda-119 \leq 0$

$	herefore \frac{1-\sqrt{239}}{2} \leq \lambda \leq \frac{1+\sqrt{239}}{2} $

$\Rightarrow-7.2 \leq \lambda \leq 8.2(	ext { nearly }) $

$	herefore \lambda=-7,-6, \ldots, 8$

The number of integral values of $\lambda $ for which $x^2 + y^2 + \lambda x + (1 - \lambda )y + 5 = 0$ is the equation of a circle whose radius cannot exceed $5$ , is

Similar Questions

The circles ${x^2} + {y^2} - 10x + 16 = 0$ and ${x^2} + {y^2} = {r^2}$ intersect each other in two distinct points, if

The equation of the image of the circle ${x^2} + {y^2} + 16x - 24y + 183 = 0$ by the line mirror $4x + 7y + 13 = 0$ is

The equation of the circle having the lines ${x^2} + 2xy + 3x + 6y = 0$ as its normals and having size just sufficient to contain the circle $x(x - 4) + y(y - 3) = 0$is

Suppose we have two circles of radius 2 each in the plane such that the distance between their centers is $2 \sqrt{3}$. The area of the region common to both circles lies between

The equation of the circle which passes through the origin, has its centre on the line $x + y = 4$ and cuts the circle ${x^2} + {y^2} - 4x + 2y + 4 = 0$ orthogonally, is