Parametric Equation of a Circle

Q. y= cos(5-3t), dy/dt=? 1. 5sin(5-3t) 2. 3sin(5-3t) 3. -5sin(5-3t) 4. -3sin(5-3t).

Q.

The line segment joining (5, 0) and (10 cos t, 10 sin t) is divided internally in the ratio 2:3 at P. If t varies, then the locus of P is

1. a circle

2. a hyperbola

3. an ellipse

4. a straight line

Q. Parametric equation of the circle, $x^2+y^2-2x+4y-11=0$ is $x=$ and $y=$ .

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

Q. { The line }2x+y=3 cuts the ellipse }4x^2+y^2=5}{ at }P and }Q . If }θ be the angle between the normals }}{ at these points, then tan }θ is equal to

Q.

If the coordinates of a point be given by the equation $x=a(1-cos\theta ),y=asin\theta$, then the locus of the point will be

1. A straight line

2. A circle

3. A parabola

4. An ellipse

Q. Let $A_0,A_1,A_2,A_3,A_4,A_5$ be a regular hexagon inscribed in a unit circle with centre at the origin. Then the product of the lengths of the line segments $A_0{A}_1,A_0{A}_2,A_0{A}_4$ is

1. 
2. 
3. 
4. 

Q.

If cos (x-y) cos(z-t) = cos(x+y) cos (z+t), then tanx tany + tanz tant is equal to

1. 1

2. -1

3. 2

4. 0

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. For the ellipse x² + 4y² = 9
(a) the eccentricity is 1/2
(b) the latus-rectum is 3/2
(c) a focus is $\left(3\sqrt{3},0\right)$
(d) a directrix is x = $-2\sqrt{3}$

Q.

What is the equation of a curve given by the parametric form $x=9+6sec\theta ;y=-2-4tan\theta$.

1. ^2}{36}-\frac{(y-2)^2}{16}=1\)

2. ^2}{36}-\frac{(y+2)^2}{16}=1\)

3. ^2}{81}-\frac{(y+4)^2}{4}=1\)

4. ^2}{81}-\frac{(y-4)^2}{4}=1\)

Q. The length of the latus-rectum of the parabola y² + 8x − 2y + 17 = 0 is
(a) 2
(b) 4
(c) 8
(d) 16

Q.

The locus of the mid point of the intersect of the variable line x cos a+ y sin a = p ( p is a constant) between the co-ordinate axes is

1. $\frac{1}{x^2}+\frac{1}{y^2}=\frac{1}{p^2}$

2. $\frac{1}{x^2}+\frac{1}{y^2}=\frac{1}{p^2}$

3. $\frac{1}{x^2}+\frac{1}{y^2}=\frac{1}{4p^2}$

4. None of these

Q.

How do you convert $r=4\sin \theta$ to rectangular form?