Chord of Contact MCQ Quiz - Objective Question with Answer for Chord of Contact - Download Free PDF
Last updated on Apr 6, 2025
Latest Chord of Contact MCQ Objective Questions
Chord of Contact Question 1:
If the circle x2 + y2 = a2 cuts off a chord of length 2b from the line y = mx + c, then
Answer (Detailed Solution Below)
Chord of Contact Question 1 Detailed Solution
For the intersection of the circle x2 + y2 = a2 and the line y = mx + c
⇒ x 2 + (mx + c)2 = a2
⇒ (1 + m2)x2 + 2mcx + c2 - a2 = 0
Let x1 and x2 be the roots of this equation,
⇒ (x1 - x2)2 = (x1 + x2)2 - 4x1x2
⇒ (x1 - x2)2 =
And since y = mx + c
⇒ y1 - y2 = m(x1 - x2) __(2)
⇒ The length of the chord =
Putting the value of (2),
⇒ 2b =
⇒
Putting the value of (1),
⇒
⇒
⇒
⇒
⇒
∴ The correct answer is option (2).
Chord of Contact Question 2:
The length of common chord of the circles (x - a)2 + y2 = a2 and x2 + (y - b)2 = b2 is
Answer (Detailed Solution Below)
Chord of Contact Question 2 Detailed Solution
Given circles, (x - a)2 + y2 = a2 and x2 + (y - b)2 = b2
⇒ x2 - 2ax + y2 = 0 and x2 + y2 - 2by = 0
Intersection of circles
⇒ ax = by
⇒
⇒ y = 0,
So points of intersection are (0,0) and (
The common chord will be the chord passing through these two points
⇒ The length of common chord =
⇒ The length of common chord =
∴ The correct answer is option (3).
Top Chord of Contact MCQ Objective Questions
Chord of Contact Question 3:
The length of common chord of the circles (x - a)2 + y2 = a2 and x2 + (y - b)2 = b2 is
Answer (Detailed Solution Below)
Chord of Contact Question 3 Detailed Solution
Given circles, (x - a)2 + y2 = a2 and x2 + (y - b)2 = b2
⇒ x2 - 2ax + y2 = 0 and x2 + y2 - 2by = 0
Intersection of circles
⇒ ax = by
⇒
⇒ y = 0,
So points of intersection are (0,0) and (
The common chord will be the chord passing through these two points
⇒ The length of common chord =
⇒ The length of common chord =
∴ The correct answer is option (3).
Chord of Contact Question 4:
If the circle x2 + y2 = a2 cuts off a chord of length 2b from the line y = mx + c, then
Answer (Detailed Solution Below)
Chord of Contact Question 4 Detailed Solution
For the intersection of the circle x2 + y2 = a2 and the line y = mx + c
⇒ x 2 + (mx + c)2 = a2
⇒ (1 + m2)x2 + 2mcx + c2 - a2 = 0
Let x1 and x2 be the roots of this equation,
⇒ (x1 - x2)2 = (x1 + x2)2 - 4x1x2
⇒ (x1 - x2)2 =
And since y = mx + c
⇒ y1 - y2 = m(x1 - x2) __(2)
⇒ The length of the chord =
Putting the value of (2),
⇒ 2b =
⇒
Putting the value of (1),
⇒
⇒
⇒
⇒
⇒
∴ The correct answer is option (2).
Chord of Contact Question 5:
The points of intersection of the line ax + by = 0, (a ≠ b) and the circle x2 + y2 - 2x = 0 are A(α, 0) and B(1, β). The image of the circle with AB as a diameter in the line x + y + 2 = 0 is :
Answer (Detailed Solution Below)
Chord of Contact Question 5 Detailed Solution
Calculation:
Given the line
Their intersection points are
Substitute
Now set
Circle with diameter
Its equation is
Reflect the centre across the line
The radius remains
Hence, the correct answer is Option 1.