1
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The parametric equations of the circle $x^2+y^2-\mathrm{a} x-b y=0$ are

A
$x=\frac{\mathrm{a}}{2}+\frac{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}{2} \cos \theta, y=\frac{\mathrm{b}}{2}+\frac{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}{2} \sin \theta$
B
$x=\frac{-\mathrm{a}}{2}+\frac{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}{4} \sin \theta, y=\frac{-\mathrm{b}}{2}+\frac{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}{4} \cos \theta$
C
$x=\frac{\mathrm{a}}{2}+\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{2}} \sin \theta, y=\frac{\mathrm{b}}{2}+\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{2}} \cos \theta$
D
$x=\frac{\mathrm{a}}{2}+\frac{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}{4} \cos \theta, y=\frac{\mathrm{b}}{2}+\frac{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}{4} \sin \theta$
2
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the tangent to the circle, given by $x=5 \cos \theta, y=5 \sin \theta$ at the point $\theta=\frac{\pi}{3}$ on it , is

A
$x-\sqrt{3} y=-5$
B
$x+\sqrt{3} y=10$
C
$\sqrt{3} x+y=5 \sqrt{3}$
D
$\sqrt{3} x-y=0$
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius $r$. If PS and RQ intersect at a point X on the circumference of the circle, then 2 r equals

A
$\sqrt{\mathrm{PQ} \cdot \mathrm{RS}}$
B
$\frac{\mathrm{PQ}+\mathrm{RS}}{2}$
C
$\frac{2 \cdot P Q \cdot R S}{P Q+R S}$
D
$\sqrt{\frac{\mathrm{PQ}^2+\mathrm{RS}^2}{2}}$
4
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The abscissae of the two points A and B are the roots of the equation $x^2+2 a x-b^2=0$ and their ordinates are roots of the equation $y^2+2 p y-q^2=0$. Then the equation of the circle with AB as diameter is given by

A
$x^2+y^2-2 \mathrm{a} x-2 \mathrm{p} y+\left(\mathrm{b}^2+\mathrm{q}^2\right)=0$
B
$x^2+y^2-2 \mathrm{a} x-2 \mathrm{p} y-\left(\mathrm{b}^2+\mathrm{q}^2\right)=0$
C
$x^2+y^2+2 \mathrm{a} x+2 \mathrm{p} y+\left(\mathrm{b}^2+\mathrm{q}^2\right)=0$
D
$x^2+y^2+2 \mathrm{a} x+2 \mathrm{p} y-\left(\mathrm{b}^2+\mathrm{q}^2\right)=0$
MHT CET Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12