﻿   Let a circle be given by                    2x (x – a) + y(2y – b) = 0            (a ≠ 0, b ≠ 0) Find the condition on a and b if two chords, each bisected by the x-axis, can be drawn to the circle from (a, b/2). : Kaysons Education

# Let A Circle Be Given By                    2x (x – a) + y(2y – b) = 0            (a ≠ 0, b ≠ 0) Find The Condition On a and b if Two Chords, Each Bisected By The x-axis, Can Be Drawn To The Circle From (a, b/2).

#### Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

#### Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

#### Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

#### National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

#### Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

#### Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

## Question

### Solution

Correct option is

The given circle is      2x (x – a) + y(2y – b) = 0

or                                x2 + y2 – ax – by/2 = 0

let AB be the chord which is bisected by x-axis at a point M. Let its co-ordinates be (h, 0)

and let

since its passes through (ab/2) we have

Now there are two chords bisected by the x-axis, so there must be two distinct real roots of h

#### SIMILAR QUESTIONS

Q1

Tangents are drawn from (6, 8) to the circle x2 + y2 = r2. Find the radius of the circle such that the areas of the âˆ† formed by tangents and chord of contact is maximum.

Q2

Find the radius of smaller circle which touches the straight line 3x – y = 6 at (1, –3) and also touches the line y = x.

Q3

2x – y + 4 = 0 is a diameter of the circle which circumscribed a rectangleABCD. If the co-ordinates of A and B are A(4, 6) and B(1, 9), find the area of rectangle ABCD.

Q4

Let 2x2 + y2 – 3xy = 0 be the equation of a pair of tangents drawn from the origin O to a circle of radius 3 with centre in the first quadrant. If A is one of the points of contact, find the length of OA.

Q5

If the circle C1x2 + y2 = 16 intersects another circle C2 of radius 5 in such a manner that the common chord is of maximum length and has a slope equal to (3/4), find the co-ordinates of centre C2.

Q6

The circle x2 + y2 = 1 cuts the x-axis at P and Q. another circle with centre at Q and variable radius intersects the first circle at R above the x-axis and the line segment PQ at S. Find the maximum area of the triangleQSR.

Q7

Find the equation of a circle having the lines x2 + 2xy + 3x + 6y = 0 as its normals and having size just sufficient to contain the circle

x(x – 4) + y(y – 3) = 0.

Q8

Find the equation of the circle whose radius is 5 and which touches the circle

x2 + y2 – 2x – 4y – 20 = 0 at the point (5, 5).

Q9

Find the locus of the mid point of the chord of the circle x2 + y2 = a2which subtend a right angle at the point (pq).

Q10

The centre of the circle S = 0 lie on the line 2x – 2y + 9 = 0 and S = 0 cuts orthogonally the circle x2 + y2 = 4. Show that circle S = 0 passes through two fixed points and find their co-ordinates.