Conic Sections Test

Result

Conic Sections Test - 56

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Weekly Quiz Competition

Question 1
1 / -0

A circle has the same center as an ellipse and passes through the foci $${ F }_{ 1 }$$, and $${ F }_{ 2 }$$, of the ellipse, such that the two curves intersect in 4 points.Let "P' be any one of their point of intersection. If the major 17 triangle $$P F _ { 1 } F _ { 2 }$$ is $$30 ,$$ then the distance between the foci is _______________.

A
11

B
12

C
13

D
none

Solution
Question 2
1 / -0

From a point P perpendiculars PM and PN are drawn to curve $$3x^2+4xy+y^2=0$$ to meet at M and N. If MN$$=2\sqrt{5}$$, then?

A
Locus of P is pair of lines

B
Locus of P is circle

C
Area bounded by locus of P and x-axis above the x-axis is $$50\pi$$

D
Distance of any tangent to locus of P from origin is $$10$$ unit

Solution
Question 3
1 / -0

Equation of the latus rectum of the hyperbola $$(10x - 5)^{2} + (10y - 2)^{2} = 9(3x + 4y - 7)^{2}$$ is

A
$$y - 1/5 =-3/4(x - 1/2)$$

B
$$x - 1/5 =-3/4(y - 1/2)$$

C
$$y + 1/5 =-3/4(x + 1/2)$$

D
$$x + 1/5 =-3/4(y + 1/2)$$

Solution
Question 4
1 / -0

If the equation $$\frac { \lambda ( x + 1 ) ^ { 2 } } { 3 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 1$$ represents a circle then $$\lambda =$$

A
1

B
$$\frac { 3 } { 4 }$$

C
0

D
$$- \frac { 3 } { 4 }$$

Solution
Question 5
1 / -0

The area enclosed between the parabolas $$y^2 = 4x$$ and $$x^2 = 4y$$ is

A
$$\dfrac{16}{3}$$ sq. unit

B
$$\dfrac{3}{4}$$ sq. unit

C
$$\dfrac{3}{16}$$ sq. unit

D
None of these

Solution
Question 6
1 / -0

Equation of the curve passing through the point $$(1,\ 2)$$ such that the intercept on the $$x-$$axis cut off between the tangent and origin is twice the abscissa is given by:

A
$$xy=2$$

B
$$xy=1$$

C
$$xy=2y$$

D
$$xy=2x$$

Solution
Question 7
1 / -0

Let $$S$$ and $$S ^ { 1 }$$ are the foci of an ellipse whose eccentricity is $$\frac { 1 } { \sqrt { 2 } } , B$$ and $$B ^ { 1 }$$ are the ends of minor axis then $$S B S ^ { \prime } B ^ { 1 }$$ forms $$a$$ ________________.

A
Parallelgram

B
Rhombus

C
Square

D
Rectangle

Solution
Question 8
1 / -0

$$D.E$$ of the curve for which the initial ordinates of any tangent is equal to the corresponding number

A
Second degree in $$x$$

B
Hemiohenous of second degree

C
Has separable variables

D
is of second degree

Solution
Question 9
1 / -0

ABCD is a square of side 1 unit. A circle passes through vertices A,B of the square and the remaining two vertices of the square lie out side the circle. The length of the tangent draw to the circle from vertex D is 2 units. The radius of the circle is

A
$$\sqrt{5}$$

B
$$\dfrac{1}{2}$$$$\sqrt{10}$$

C
$$\dfrac{1}{3}$$$$\sqrt{12}$$

D
$$\sqrt{8}$$

Solution
Question 10
1 / -0

The coordinates of the foci of the hyperbola $$xy=c^2$$ are

A
$$(\pm C, \pm C)$$

B
$$(\pm \dfrac{c}{\sqrt{2}}< \pm\dfrac{c}{\sqrt{2}})$$

C
$$(\pm 2c, \pm 2c)$$

D
$$(\pm \sqrt{2}c, \pm \sqrt{2}c)$$

Solution