Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
78.9k views
in Mathematics by (88.9k points)

If two distinct chords, drawn from the point ( p , q) on the circle x2 + y2 = px + qy (where pq ≠ 0) are bisected by the x-axis, then

(a) p2 = q2

(b) p2 = 8q2 

(c) p2 < 8q2

(d) p2 > 8q2

1 Answer

+1 vote
by (79.0k points)
selected by
 
Best answer

Correct option: (d) p2 > 8q2

Explanation:

In solving a line and a circle there often generate a quadratic equation and further we have to apply condition of Discriminant so quation convert from coordinate to quadratic equation.

From equation of circle it is clear that circle passes through origin. Let AB is chord of the circle.

A ≡ (p, q). C is mid point and coordinate of C is (h, 0).

Then coordinate of B are (-p + 2h, -q) and B lies on the circle

x2 + y2 = px + qy, we have

There are given two distinct chords which are bisected at x-axis then, there will be two distinct values of h satisfying Eq. (i).

So, discriminant of this quadratic equation must be > 0.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...