The value of for which the equation 2 (x^2+y^2 )- 6 x+8 y+ =0 rep… - Vidyadip

MCQ

The value of $\lambda$ for which the equation $2\left(x^2+y^2\right)-$ $6 x+8 y+\lambda=0$ represents a point circle is

A
$\frac{25}{4}$
B
$\frac{4}{25}$
✓
$\frac{25}{2}$
D
$\frac{2}{25}$

✓

Answer

Correct option: C.

$\frac{25}{2}$

(C) $\frac{25}{2}$
Explanation : Given equation of circle is
$2\left(x^2+y^2\right)-6 x+8 y+\lambda=0$
or, $\left(x^2+y^2\right)-3 x+4 y+\frac{\lambda}{2}=0\quad \ldots(i) $
If the radius of the circle is zero, then the circle is called a point circle. Thus, eq. (i) will represents a point circle, if
$
\sqrt{\left(\frac{3}{2}\right)^2+(-2)^2-\frac{\lambda}{2}}=0\left[\because r=\sqrt{g^2+f^2-c}\right]
$
$\begin{array}{ll}\Rightarrow & \frac{\lambda}{2}=\frac{25}{4} \\ \Rightarrow & \lambda=\frac{25}{2}\end{array}$

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

More "MCQ" from Circles→Circles — all question types→Applied Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

For any two events A and B, if $\mathrm{P}(\overline{\mathrm{A}})=\frac{1}{2}, \mathrm{P}(\overline{\mathrm{B}})=\frac{2}{3}$ and $\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{4}$, then $\mathrm{P}\left(\frac{\overline{\mathrm{A}}}{\overline{\mathrm{B}}}\right)$ equals:

If $P\left(\frac{A}{B}\right)>P(A)$, then which of the following is correct :

Which of the following is not a binary number?

Let $f$ and $g$ be real function be $f(x)=\sqrt{x+4}, x \geq-4$ and $g(x)=\sqrt{x-4}, x \geq 4$. Then function $f g$ is

Relationship between annual nominal rate of interest and annual effective rate of interest, if frequency of compounding is greater than one:

If the relation $R$ in the set $\{1,2,3,4\}$ given by $R=\{(1,1),(1,2),(1,4),(3,1),(3,2),(4,3),(4,2)\}$ then domain of $R$ is given by

$\log _{10} 0.0001$ is equal to

What does the P stands for in this formula?
Present value $=P\left[\frac{1-(1+i)^n}{i}\right]$

A retailer purchases a fan for $₹ 1500$ from a wholesaler and sells it to a consumer at $10 \%$ profit. If the sales are intra-state and the rate of GST is $12 \%$, the selling price of the fan by the retailer (excluding tax) is:

Bag A contains 3 red and 5 black balls and bag B contains 2 red and 4 black balls. A ball is drawn from one of the bags. The probability that ball drawn is red is