Use app×
JEE MAIN 2024
JEE MAIN 2025 Foundation Course
NEET 2024 Crash Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
1.1k views
in Mathematics by (23.9k points)

Intercepts made on the axes by the circle whose equation is ax2 + ay2 + 2gx + 2fy + c = 0.

1 Answer

+1 vote
by (34.3k points)
selected by
 
Best answer

ax2 + ay2 + 2gx + 2fy + c = 0....(1)

The abscissa of the points where the circle (1) meets the axis of x i.e. y = 0, are given by the equation

ax2 + 2gx + c = 0  .......(2)

The roots of this equation being x1 and x2 we have

Again, the roots of the equation (2) are both imaginary if g2 < ac. In this case the circle does not meet the axis of x in real points, i.e. geometrically it does not meet the axis of x at all.

The circle will touch the axis of x if the intercept A1A2, be just zero, i.e. ii g2 = ac.

It will meet the axis of x in two points lying on opposite sides of the origin if the two roots of the equation (2) are of opposite signs, i.e. if c be negative.

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

...