Parametric Equation of a Circle

Q.

Find the parametric equation of the circle $x^2+y^2-2x+4y-11=0$

1. $x=-2+4cos\theta andy=+4+4cos\theta$

2. $x=-2+4cos\theta andy=+4+4cos\theta$

3. $x=-1+4cos\theta andy=+2+4sin\theta$

4. $x=1+4cos\theta andy=-2+4sin\theta$

Q.

Parametric equation of $(x-h{)}^2+(y-k{)}^2=r^{2}arex+h=rcos\theta andy+k=rsin\theta$

1. True

2. False

Q. If a straight line through $C(-\sqrt{8},\sqrt{8})$ making an angle ${135}^{\circ }$ with the x-axis cuts the circle $x=5cos\theta ,y=5sin\theta$ in points A and B, then length of segment AB is

1. 15
2. 5
3. 10
4. 

Q.

A circle with centre at the origin and radius equal to a meets the axis of x and A and B. $P\left(\alpha \right)$ and $Q\left(\beta \right)$ are two points on this circle so that $\alpha -\beta =2\gamma$, where $\gamma$ is a constant. The locus of the point of intersection of AP and BQ is

1. 
2. 
3. 
4. 

Q. The center of the circle given by the parametric equation x = -1 + 2 cos $\theta$, y = 3 + 2sin $\theta$ is (-1, 3).

1. False
2. True

Q. The parametric eqauation of the circle $x^2+y^2-2x-4y-4=0$ is .

1. $x=1-3\cos \theta ,y=2+3\sin \theta$
2. $x=1+3\cos \theta ,y=2-3\sin \theta$
3. $x=1+3\cos \theta ,y=2+3\sin \theta$
4. $x=1-3\cos \theta ,y=2-3\sin \theta$

Q. Let $x$, $y$ be real variables satisfying the equation $x^2+y^2+8x-10y+40=0$. If $a=max\left\{\right(x+2{)}^2+(y-3{)}^2\}$ and $b=min\left\{\right(x+2{)}^2+(y-3{)}^2\}$, then

1. $a+b=18$
2. $a+b=\sqrt{2}$
3. $a-b=4\sqrt{2}$
4. $ab=73$

Q. If the parametric equation of a circle are $x=-4+5\cos \theta$ and $y=-3+5\sin \theta$, then which of the following is/are true

1. centre of circle is $(4,3)$
2. centre of circle is $(-4,-3)$
3. area of circle is $25\pi$ sq.units
4. perimeter of circle is $10\pi$ units

Q. Equation of circle whose parametric equations are $x=5-5\sin t$ and $y=4+5\cos t$ is

1. $(x+5{)}^2+(y-4{)}^2=25$
2. $(x-5{)}^2+(y+4{)}^2=25$
3. $(x+5{)}^2+(y+4{)}^2=25$
4. $(x-5{)}^2+(y-4{)}^2=25$

Q. The centre of the circle $x=1+2\cos \theta ,y=-3+2\sin \theta ,$ is

1. $(-1,3)$
2. $(1,-3)$
3. $(2,3)$
4. $(-\frac{1}{2},\frac{3}{2})$