Conic Sections Test

Result

Conic Sections Test - 58

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Weekly Quiz Competition

Question 1
1 / -0

The latus rectum of a conic section is the width of the function through the focus. The positive difference between the length of the latus rectum of $$3y =x^{2}+4x-9$$ and $$x^{2}+4y^{2}-6x+16y =24$$ is-

A
$$\frac{1}{2}$$

B
2

C
$$\frac{3}{2}$$

D
$$\frac{5}{2}$$

Solution
Question 2
1 / -0

If the line $$3x+4y=1$$ touches the parabola $$y^{2}=4ax$$ then length of its latus rectum is equal to

A
$$3/16$$

B
$$3/8$$

C
$$3/4$$

D
$$9/16$$

Solution
Question 3
1 / -0

The parabola $$y^{6}=4ax$$ passes through the point $$(2,-6)$$, then the length of its latus rectum is

A
$$18$$

B
$$9$$

C
$$6$$

D
$$16$$

Solution
Question 4
1 / -0

The length of the latus rectum of the parabola $$x^2=ay+by+c$$ is

A
$$\dfrac{a}{4}$$

B
$$\dfrac{a}{3}$$

C
$$\dfrac{1}{a}$$

D
$$\dfrac{1}{4a}$$

Solution
Question 5
1 / -0

A tangent drawn to hyperbola $$\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}=1$$ at $$P\left(\dfrac{\pi}{6}\right)$$ forms a triangle of area $$3a^{2}$$ square units, with coordinate axes. Its eccentricity is equal to

A
$$4$$

B
$$5$$

C
$$\dfrac{9}{2}$$

D
$$\sqrt{17}$$

Solution
Question 6
1 / -0

The name of the conic whose focus is $$\left(-1,1\right)$$ corresponding direction is $$x-y+1=0$$ whose length of semi latusrectum is $$3$$, is

A
Parabola

B
Ellipse

C
Hyperbola

D
Pair of lines

Solution
Question 7
1 / -0

In the line $$2x+3y=1$$ touches the parabola $$y^{2}=4a(x+a)$$, then the length of its latus rectum is

A
$$\dfrac {8}{9}$$

B
$$\dfrac {8}{13}$$

C
$$4$$

D
$$\dfrac {4}{9}$$

E
$$\dfrac {4}{13}$$

Solution
Question 8
1 / -0

The equation $$y = \sqrt{2 - x^2 - y^2} + \sqrt{x^2 + y^2 - 2}$$ represents, where $$x > 0$$

A
Circle with radius $$2$$ units

B
Parabola

C
A point circle

D
Ellipse

Solution
Question 9
1 / -0

A tangent to the curve y = f(x) cuts the line y = x at a point which is at a distance of 1 unit from y - axis. The equation of the curve is

A
$$\dfrac{x - 1}{y - 1} = C$$

B
$$\dfrac{x}{y} = C$$

C
$$xy = C$$

D
none of these

Solution
Question 10
1 / -0

The length of the latus rectum of the parabola $$x^2-4x-8y+12=0$$ is

A
4

B
6

C
8

D
2

Solution