If the line 3x - 4y = touches the circle x^2 + y^2 - 4x - 8y - 5 … - Vidyadip

MCQ

If the line $3x - 4y = \lambda $ touches the circle ${x^2} + {y^2} - 4x - 8y - 5 = 0$, then $\lambda $ is equal to

A
$-35, -15$
✓
$-35, 15$
C
$35, 15$
D
$35,-15$

✓

Answer

Correct option: B.

$-35, 15$

b
(b) Accordingly, $\frac{{3(2) - 4(4) - \lambda }}{{\sqrt {{3^2} + {4^2}} }} $

$= \pm \sqrt {{2^2} + {4^2} + 5} $

$ \Rightarrow - 10 - \lambda = \pm 25$

$\Rightarrow \lambda = - 35,\;15$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If ${C_0},{C_1},{C_2},.......,{C_n}$ are the binomial coefficients, then $2.{C_1} + {2^3}.{C_3} + {2^5}.{C_5} + ....$ equals

If two straight lines whose direction cosines are given by the relations $l+m-n=0,3l^{2}+m^{2}+c n l =0$ are parallel, then the positive value of $c$ is

Let the vectors $\overrightarrow{ u }_1=\hat{ i }+\hat{ j }+ a \hat{ k }, \overrightarrow{ u }_2=\hat{ i }+ b \hat{ j }+\hat{ k }$ and $\overrightarrow{ u }_3=c \hat{ i }+\hat{ j }+\hat{ k }$ be coplanar. If the vectors $\overrightarrow{ v }_1=(a+b) \hat{i}+c \hat{j}+c \hat{k}, \quad \overrightarrow{ v }_2=a \hat{i}+(b+c) \hat{j}+a \hat{k} \quad$ and $\overrightarrow{ v }_3=b \hat{ i }+ b \hat{ j }+( c + a ) \hat{ k }$ are also coplanar, then $6( a +$ $b + c )$ is equal to $..............$.

In the interval $(0, 1)$ maximum value of the function $f (x) = |x\ ln\ x|$ is

Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}-\hat{k}$ be three vectors. A vector $\vec{v}$ in the plane of $\vec{a}$ and $\vec{b}$, whose projection on $\vec{c}$ is $\frac{1}{\sqrt{3}}$, is given by

Let $[x]$ denotes the greatest integer less than or equal to $x$. If $f(x) = [x\sin \pi x]$, then $f(x)$ is

If $a,b,c,d,e$ are in $A.P.$ then the value of $a + b + 4c$ $ - 4d + e$ in terms of $a$, if possible is

If three positive numbers $a, b$ and $c$ are in $A.P.$ such that $abc\, = 8$, then the minimum possible value of $b$ is

The equation of the curve passing through the origin and satisfying the differential equation $\left( {1 + {x^2}} \right)\,\frac{{dy}}{{dx}} + 2xy = 4{x^2}$ is

If the line $x - 2y = k$ cuts off a chord of length $2$ from the circle ${x^2} + {y^2} = 3$, then $k =$