Conic Sections Test

Result

Conic Sections Test - 62

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Weekly Quiz Competition

Question 1
1 / -0

Length of the latus rectum of the hyperbola $$ x y=c^{2}, $$ is

A
$$\sqrt{2} {c}$$

B
$$2c$$

C
$$2\sqrt{2}{c}$$

D
$$4c$$

Solution
Question 2
1 / -0

Let $$PQ$$ be a variable focal chord of the parabola $${y^2} = 4ax\left( {a > 0} \right)$$ whose vertex is A. then the locus of centroid of $$\Delta APQ$$ lies on a parabola whose length of latusrectum is

A
$$\frac{{2a}}{3}$$

B
a

C
$$\frac{{4a}}{3}$$

D
$$\frac{{5a}}{3}$$

Solution
Question 3
1 / -0

Lissajous figure obtained by combining x=ASin $$\omega t$$ and y=ASin $$(\omega t+\Pi /4)$$ will be

A
an ellipse

B
a straight line

C
a circle

D
a parabola

Solution
Question 4
1 / -0

The equations $$x=\dfrac{t}{4}, y=\dfrac{t^2}{4}$$ represents

A
An ellipse

B
A parabola

C
A circle

D
A hyperbola
Question 5
1 / -0

$$If$$ $${y^2} - 2x - 2y + 5 = 0$$ is

A
$$a\,\,circle\,with\,centre\,(1,1)$$

B
$$a\,\,parabola\,with\,\,vertex\,(1,2)$$

C
$$a\,parabola\,with\,directrix\,x = \frac{3}{2}$$

D
$$a\,parabola\,with\,directrix\,x = - \frac{1}{2}$$

Solution
Question 6
1 / -0

The value of $$\alpha $$ for which three distinct chords drawn from $$(\alpha ,0)$$ to the ellipse $${ x }^{ 2 }+2{ y }^{ 2 }=1$$ are bisected by the parabola $${ y }^{ 2 }=4x$$ is

A
$$9$$

B
$$\sqrt { 17 } $$

C
$$8$$

D
None of these.
Question 7
1 / -0

A circle passes through $$A(1,2)$$ and the equations of the normal to the circle is $$x+2y=5$$. If the circle passes through $$B(-5,5)$$, then the radius of the circle is

A
$$\dfrac {3}{2}$$

B
$$\dfrac {\sqrt {5}}{2}$$

C
$$\dfrac {3\sqrt {5}}{2}$$

D
$$\dfrac {5}{2}$$

Solution
Question 8
1 / -0

Let PQ be the latus rectum of the parabola $$y^2=4x$$ with vertex A. Minimum length of the projection of PQ on a tangent drawn in portion of parabola PAQ is :

A
$$2$$

B
$$4$$

C
$$2 \sqrt{3}$$

D
$$2 \sqrt{2}$$

Solution
Question 9
1 / -0

If the radius of the circle $${x}^{2}+{y}^{2}+2gx+2fy+c=0$$ be $$r$$, then it will touch both the axes, if

A
$$g=f=c$$

B
$$g=f=c=r$$

C
$$g=f=\sqrt{c}=r$$

D
$$g=f$$ and $${c}^{2}=r$$
Question 10
1 / -0

If two distinct chords of a parabola $$y^2 = 4 \,ax$$ passing through the point $$(a, 2a)$$ are bisected by the line $$x + y = 1$$, then the length of the latus rectum can be

A
$$(2,6)$$

B
$$(1,4)$$

C
$$(0,2)$$

D
$$(0,4)$$

Solution