Chapter 5: Two Dimensional Analytical Geometry II - Online Test
Q1. 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
= r 2 , then the value of r 2 is
Answer : Option A
Explaination / Solution:
Q2. If x + y = k
is a normal to the parabola y2 = 12x , then the
value of k is
Answer : Option D
Explaination / Solution:
Q3. The ellipse E1 : 
is inscribed in a rectangle
R whose sides are parallel to the coordinate axes. Another ellipse E2
passing through the point (0, 4) circumscribes the rectangle R . The eccentricity of the ellipse is
is inscribed in a rectangle
R whose sides are parallel to the coordinate axes. Another ellipse E2
passing through the point (0, 4) circumscribes the rectangle R . The eccentricity of the ellipse is
Answer : Option C
Explaination / Solution:
Q4.
Tangents are drawn to
the hyperbola 
parallel to the straight line 2x − y =
1. One ofthe points of contact of tangents on the hyperbola is
Answer : Option C
Explaination / Solution:
Q5. The equation of the circle
passing through the foci of the ellipse 
having centre at (0,3) is
having centre at (0,3) is
Answer : Option A
Explaination / Solution:
Q6. Let C be the circle
with centre at (1,1) and radius = 1 . If T is the circle centered at (0,
y) passing through the origin and touching the circle C externally,
then the radius of T is equal to
Answer : Option D
Explaination / Solution:
Q7. Consider an ellipse whose
centre is of the origin and its major axis is along x-axis. If its
eccentrcity is 3/5 and the distance between its foci is 6, then the area of the
quadrilateral inscribed in the ellipse with diagonals as major and minor axis
of the ellipse is
Answer : Option D
Explaination / Solution:
Q8. Area of the greatest
rectangle inscribed in the ellipse 
is
is
Answer : Option A
Explaination / Solution:
Q9. An ellipse has OB as
semi minor axes, F and F ′ its foci and the angle FBF ′ is
a right angle. Then the eccentricity of the ellipse is
Answer : Option A
Explaination / Solution:
Q10. The eccentricity of the
ellipse (x - 3)2 + ( y - 4)2 = y2/9 is
Answer : Option B
Explaination / Solution:
