Question

PLEASE HELP

Answer 1

Answer:

11. Equation of hyperbola having  vertices at (0, ±6) and foci at (0, ±9).

is given by $\frac{y^2}{a^2}- \frac{x^2}{b^2}=1$

also b²= c²-a²

 b²=81-36

b²=45

So, Equation becomes , $\frac{y^2}{36}- \frac{x^2}{45}=1$

Option (D) is correct.

12.Vertices (0,  ± 4), Asymptotes = ±1/4.x

equation of asymptote is given by, $x = \pm y \frac{b}{a}$

$\frac{4}{b}=\frac{1}{4}$

So a=4 and b=16,

So , equation becomes $\frac{y^2}{16}- \frac{x^2}{256}=1$

Option (B) is correct.

13.  x= t-3, and y = t²+ 5

Replace t by x+3, we get

y= (x+3)² +5

y=x²+ 6x +14

Option (A) is correct.

14. Polar coordinates is given by (r,∅)

Polar coordinates of point is (3, 2π/3)

So, r =3, ∅ =2π/3

x= r cos∅ and y = r sin∅

x=3 Cos (2π/3) and y= 3 Sin (2π/3)

x= -3/2 and y=3√3/2

Option (A) is correct.

14. Polar coordinate is given by (r,∅)

Here , r=1, and ∅ = -π/6

x= r Cos ∅ and y =r Sin∅

x= 1 Cos (-π/6) and  y= 1 Sin (-π/6)

x =√3/2 and y =1/2

Option (B) which is B) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + 2nπ) is correct.

16. Two pairs of polar coordinates for the point (4, 4) with 0° ≤ θ < 360°.

is  option (B) which is B) (4 square root 2 , 45°), (-4 square root 2 , 225°).

17. A circular graph with inner loop on the left of a limacon curve is given by

r = a + b Cos∅.

In this case a> b.

So , Option (D) r = 4 + cos θ as well as (A) r = 3 + 2 cos θ looks correct.

18. Equation of limacon curve is given by r = -2 + 3 cos θ, here , a<b

So it is symmetric about y-axis only.Option (B) is correct.