Question

# Match the following by approximately matching the lists based on the information given in Column I and Column II Column 1Column 2a. The length of the common chord of two circles of radii 3 and p. 14 units which intersect orthogonally is k5,then k is equal to b. The circumference of the circle x2+y2+4x+12y+p=0 q. 24 is bisected by the circle x2+y2−2x+8y−q=0, then p+q is equal to c. Number of distinct chords of the circle 2x(x−√2)+y(2y−1)r. 32=0 chords are passing through the point (√2,12) and are bisected on x-axis is d. One of the diameters of the circle circumscribing the rectangle s. 36ABCD is 4y=x+7. If A and B are the points (−3,4) and (5,4) respectively, then the area of rectangle is

A
aq, bs, cp, dr
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
ap, bs, cq, dr
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
aq, br, cp, ds
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
ar, bs, cp, dq
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A a−q, b−s, c−p, d−r (a) Let the length of the common chord be 2a. Then, √9−a2+√16−a2=5 or √16−a2=5−√9−a2 or 16−a2=25+9−a2−10√9−a2 or 10√9−a2=18 or 100(9−a2)=324 or 100a2=576 or a=√576100=2410 ∴2a=245=k5⇒k=24 (b) The equation of common chord is 6x+4y+p+q=0 The common chord passes through the center (−2,−6) of the circle x2+y2+4x+12y+p=0. Therefore, p+q=36 (c) The equation of the circle is 2x2+2y2−2√2x−y=0 let (α,0) be the midpoint of a chord. Then, the equation of the chord is 2αx−√2(x+α)−12(y+0)=2α2−2√2α Since it passes through the point (√2,12), we have 2√2α−√2(√2+α)−14=2α2−2√2α ⇒8α2−12√2α+9=0 ⇒(2√2α−3)2=0 α=32√2,32√2 Therefore, the number of chords is 1 (d) Midpoint of AB≡(1,4) The equation perpenduicular bisector of AB is x=1 A dimeter of the circle is 4y=x+7 Therefore, the center of the circle is (1,2) Hence, the sides of the rectangle are 8 and 4. Therefore, Area =32

Suggest Corrections
0
Join BYJU'S Learning Program
Select...
Related Videos
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program
Select...