Centre of circle whose normals are x^2- 2xy - 3x + 6y = 0, is: - Vidyadip

MCQ

Centre of circle whose normals are $x^2- 2xy - 3x + 6y = 0$, is:

✓
$\big(3, \frac{3}{2}\big)$
B
$\big(3, -\frac{3}{2}\big)$
C
$\big(\frac{3}{2},3\big)$
D
None of these

✓

Answer

Correct option: A.

$\big(3, \frac{3}{2}\big)$

$x^2- 2xy - 3x + 6y = 0$
$\Rightarrow (x - 3) (x - 2y) = 0$
$\Rightarrow x = 3$ and $x = 2y$ are two normals.
The intersection point of these two normals will be the centre of the circle.
$\therefore$ for $x = 3$
$\Rightarrow\text{y}=\frac{\text{x}}{2} = \frac{3}{2}$
The intersection point is $\big(3, \frac{3}{2}\big)$ the centre of the given circle is $\big(3, \frac{3}{2}\big)$

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 "M.C.Q (1 Marks)" from Conic Sections→Conic Sections — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

$B\,\, \& \,\,C$ are fixed points having co-ordinates $(3, 0)$ and $(- 3, 0)$ respectively . If the vertical angle $BAC$ is $90^o$, then the locus of the centroid of the $\Delta ABC $ has the equation :

In how many ways can Rs. $16$ be divided into $4$ person when none of them get less than Rs. $3$

The number of ways of dividing $52$ cards amongst four players equally, are

In the Argand plane, the vector $z = 4 - 3i$ is turned in the clockwise sense through ${180^o}$and stretched three times. The complex number represented by the new vector is

Let $a,b,c$ be real numbers $a \ne 0$. If $\alpha $is a root ${a^2}{x^2} + bx + c = 0$, $\beta $ is a root of ${a^2}{x^2} - bx - c = 0$ and $0 < \alpha < \beta $, then the equation ${a^2}{x^2} + 2bx + 2c = 0$ has a root $\gamma $ that always satisfies

If $x-$coordinate of a point $P$ of line joining the points $Q(2, 2, 1)$ and $R(5, 2, -2)$ is $4,$ then the $z-$coordinate of $P$ is:

The probabilities of occurrence of two events are respectively $0.21$ and $0.49$. The probability that both occurs simultaneously is $0.16$. Then the probability that none of the two occurs is

The set of all real numbers $x$ for which ${x^2} - |x + 2| + x > 0,$ is

If $\cos (\alpha - \beta ) = 1$ and $\cos (\alpha + \beta ) = \frac{1}{e}$, $ - \pi < \alpha ,\beta < \pi $, then total number of ordered pair of $(\alpha ,\beta )$ is

If $\theta $ and $\phi $ are eccentric angles of the ends of a pair of conjugate diameters of the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, then $\theta - \phi $ is equal to