Conic Sections - Online Test

Q1. The value of k, such that the equation   represents a point circle, is
Answer : Option B
Explaination / Solution:


which gives radius  for a point circle radius should be zero.
hence 
solving which we get k=

Q2. The equation  represents a circle only if
Answer : Option D
Explaination / Solution:

recalling the general form of a circle as

(i) It is a quadratic equation in both x and y.

(ii) Coefficient of   = Coefficient of    .

(iii) There is no term containing xy i.e., the coefficient of xy is zero.

(iv) radius is  

To satisfy (i) and (ii) condition we have  

To satisfy (iii) condition we have 

To satisfy (iv) and as we cant have neagtive sign in root so 


Q3.

 is a circle. The points (0, 0) and ( 1, 8) lie


Answer : Option B
Explaination / Solution:


so the center is (3,-4) and radius is 6 units.
distance between center and (0,0) is  units which is less than the radius so it lies inside the circle
whereas the distance between center and (1,8) is  which is greater than the radius so it lies outside the circle

Q4. Which one of the following lines is farthest from the centre of the circle 
Answer : Option D
Explaination / Solution:


after completing the square,we get 

so center is (0,0) and equation of given line is  by applying  formula of distance of a point from a given line i.e.,  where(x1,y1) are the coordinates of point and A and B are coefficient of x,y in given line so d = 
  which is greatest.
Q5. The length of the common chord of the parabolas  and  is
Answer : Option D
Explaination / Solution:

point  of intersection is (0,0) and (1,1). Hence by using the  distance formula


Q6. The number of points on X-axis which are at a distance c units (c 3) from ( 2, 3) is
Answer : Option B
Explaination / Solution:

the shortest distance from x-axis to the point is 3.

Q7. The eccentricity of the conic  is
Answer : Option D
Explaination / Solution:

Given 9x2 - 16y2 = 144

Dividing throughout by 144 we get,

 -  = 1

This implies a2 = 16 and b2 = 9

e =  = 


Q8. The eccentricity of  is
Answer : Option B
Explaination / Solution:

Given equation is 3x2 + 4y2 = 24

dividing throught by 24 we get,

 +  = 1

This implies a2 = 8 and b2 = 6

e =  =


Q9. The angle between the tangents drawn from the origin to the circle =  is
Answer : Option B
Explaination / Solution:

The angle between the Radius and tangent is 900

Q10. The line y = mx + 1 is a tangent to the parabola  if m =
Answer : Option B
Explaination / Solution:

The contion for a line to be a tangent to the parabola is y = mx +

From the given equation of the parabola we infer that a = 1 and from the equation of the line c = 1

Therefore m = a/c = 1