Conic Sections Test

Result

Conic Sections Test - 42

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Weekly Quiz Competition

Question 1
1 / -0

The eq. of the circle which touches the exes of y at a distance of $$4$$ from the origin and cuts the intercepts of $$6$$ units from the axis of x is

A
$$x^2 +y^2 \pm 10x \pm 8y + 16=0$$

B
$$x^2 +y^2 \pm 5x \pm 4y + 16=0$$

C
$$x^2 +y^2 \pm 10x \pm 8y - 16=0$$

D
$$x^2 +y^2 \pm 5x \pm 4y - 16=0$$

Solution
Question 2
1 / -0

$$AB$$ is a diameter of $$x^{2}+9y^{2}=25$$. The eccentric angle of $$A$$ is $$\dfrac{\pi}{6}$$. Then the eccentric angle of $$B$$ is

A
$$\dfrac{5\pi}{6}$$

B
$$\dfrac{-5\pi}{6}$$

C
$$\dfrac{-2\pi}{3}$$

D
$$\dfrac{\pi}{3}$$

Solution
Question 3
1 / -0

Let $$P,\ Q,\ R,\ S$$ be the feet of perpendicular drawn from the point $$(1,\ 1)$$ the lines $$y=3x+4$$ and $$y=-3x+6$$ and their angle bisectors respectively, the equation of the circle whose extremities of a diameter are $$R$$ and $$S$$ is

A
$$3x^{2}+3y^{2}+104x-110=0$$

B
$$x^{2}+y^{2}+104x-110=0$$

C
$$3x^{2}+3y^{2}-4x-18y+16=0$$

D
$$x^{2}+y^{2}-4x-18+16=0$$

Solution
Question 4
1 / -0

The length of the latus rectum of the parabola whose focus is (3,0) and directrix is 3x-4y-2=0 is

A
12

B
1

C
4

D
none of these

Solution

focus $$\equiv (a,0)$$ . $$f\equiv (3,0)$$
$$\therefore a=3$$

Length of latus rectum $$= 4a$$
$$= 4\times 3$$
$$= 12$$ cm
Question 5
1 / -0

The area bounded by the parabola $${ y }^{ 2 }=4xy\quad $$ and its rectum is :-

A
$$\frac { { 4 }^{ a } }{ 3 } sq-units$$

B
$$\frac { { 8a }^{ 2 } }{ 3 } sq-units$$

C
$$\frac { { 4a }\sqrt { a } }{ 3 } sq-units$$

D
$$\frac { { 8a }\sqrt { a } }{ 3 } sq-units$$

Solution
Question 6
1 / -0

A parabola passing through the point $$(-4,-2)$$ has its vertex at the origin and $$y-$$axis as its axis. The latus rectum of the parabola is

A
$$6$$

B
$$8$$

C
$$10$$

D
$$12$$

Solution
Question 7
1 / -0

The equation of the latusrectum of the parabola $${ x }^{ 2 }+4x+2y=0$$ is:-

A
3y-2=0

B
3Y+2=0

C
2Y-3=0

D
2Y+3=0

Solution
Question 8
1 / -0

The equation of the circle having as a diameter, the chord $$x - y - 1 = 0$$ of the circle $$2x^2 + 2y^2 - 2x - 6y - 25 = 0$$, is

A
$$x^2 + y^2 - 3x - y - \dfrac{29}{2} = 0$$

B
$$2x^2 + 2y^2 + 2x - 5y - \dfrac{29}{2} = 0$$

C
$$2x^2 + 2y^2 - 6x - 2y - 21 = 0$$

D
None of these

Solution
Question 9
1 / -0

The curve represented by $$Rs \left(\dfrac{1}{z}\right)=C$$ is (where $$C$$ is a constant and $$\neq 0$$)

A
Ellipse

B
Parabola

C
Circle

D
Straight line

Solution

$$\begin{array}{l} { { Re } }\, \, \left( { \frac { 1 }{ z } } \right) =c \\ { { Re } }\, \, \left( { \frac { 1 }{ { x+iy } } } \right) =c \\ { { Re } }\, \, \left( { \frac { { x-iy } }{ { { x^{ 2 } }+{ y^{ 2 } } } } } \right) =c \\ \frac { x }{ { { x^{ 2 } }+{ y^{ 2 } } } } =c \\ c\left( { { x^{ 2 } }+{ y^{ 2 } } } \right) -{ x }=0 . \end{array}$$

Hence, this is represent circle.
Question 10
1 / -0

The intercept on the line $$y = x$$ by the circle $${x^2} + {y^2} - 2x = 0$$ is $$AB$$. The equation of the circle with $$AB$$ as a diameter, is

A
$${x^2} + {y^2} + x + y = 0$$

B
$${x^2} + {y^2} = x + y$$

C
$${x^2} + {y^2} - 3x + y = 0$$

D
None of the above

Solution

Hence, Option (B) is the correct answer.