12th Standard Maths Two Dimensional Analytical Geometry-II English Medium Free Online Test One Mark Questions 2020 - 2021

12th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

10 x 1 = 10
1. The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

(a)

$0,-\frac { 40 }{ 9 }$

(b)

0

(c)

$\frac { 40 }{ 9 }$

(d)

$\frac { -40 }{ 9 }$

2. The radius of the circle3x2+by2+4bx−6by+b2 =0 is

(a)

1

(b)

3

(c)

$\sqrt {10}$

(d)

$\sqrt {11}$

3. The equation of the normal to the circle x2+y2−2x−2y+1=0 which is parallel to the line
2x+4y=3 is

(a)

x+2y=3

(b)

x+2y+3= 0

(c)

2x+4y+3=0

(d)

x−2y+3= 0

4. If the normals of the parabola y2 = 4x drawn at the end points of its latus rectum are tangents to the circle (x−3)2+(y+2)2=r2 , then the value of r2 is

(a)

2

(b)

3

(c)

1

(d)

4

5. The equation of the circle passing through the foci of the ellipse  $\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1$ 1having centre at
(0,3) is

(a)

x2+y2−6y−7=0

(b)

x2+y2−6y+7=0

(c)

x2+y2−6y−5=0

(d)

x2+y2−6y+5=0

6. If the two tangents drawn from a point P to the parabolay2 = 4x are at right angles then the locus of P is

(a)

2x+1=0

(b)

x = −1

(c)

2x−1=0

(d)

x =1

7. If (0, 4) and (0, 2) are the vertex and focus of a parabola then its equation is

(a)

x2 + 8y = 32

(b)

y2 + 8x = 32

(c)

x2 - 8y= 32

(d)

y2 - 8x = 32

8. Equation of tangent at (-4, -4) on x2 = -4y is

(a)

2x - y + 4 = 0

(b)

2x + y - 4 = 0

(c)

2x - y - 12 = 0

(d)

2x + y + 4 = 0

9. In an ellipse, the distance between its foci is 6 and its minor axis is 8, then e is

(a)

$\frac { 4 }{ 5 }$

(b)

$\frac { 1 }{ \sqrt { 52 } }$

(c)

$\frac { 3 }{ 5 }$

(d)

$\frac { 1 }{ 2 }$

10. The locus of the foot of perpendicular from the focus on any tangent to y2 = 4ax is

(a)

x2 + y2 = a2 - b2

(b)

x2 + y2 = a2

(c)

x2 + y2 = a2 - b2

(d)

x = 0