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Find the length of the common chord of the circles {x}^{{2}}+{

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Find the length of the common chord of the circles $x^{2} + y^{2} + 2 x + 6 y = 0$ and $x^{2} + y^{2} - 4 x - 2 y - 6 = 0$

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Find the length of the common chord of the circles

x^{2} + y^{2} + 2 x + 6 y = 0

and

x^{2} + y^{2} - 4 x - 2 y - 6 = 0

15 mins ago

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Practice questions from similar books

Question 1

Let P and Q be distinct points on the parabola

y^{2} = 2 x

such that a circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle

Δ O P Q

32

, then which of the following is (are) the coordinates of

P ?

View solution

Question 2

Consider two straight lines, each of which is tangent to both the circle

x^{2} + y^{2} = \frac{1}{2}

and the parabola

y^{2} = 4 x

. Let these lines intersect at the point

Q

. Consider the ellipse whose center is at the origin

O (0, 0)

and whose semi-major axis is

O Q

. If the length of the minor axis of this ellipse is

2

, then which of the following statement(s) is (are) TRUE?For the ellipse, the eccentricity is

\frac{1}{2}

and the length of the latus rectum is 1(b) For the ellipse, the eccentricity is

\frac{1}{2}

and the length of the latus rectum is

\frac{1}{2}

x = \frac{1}{2}

and

x = 1

\frac{1}{4 2} (π - 2)

(d) The area of the region bounded by the ellipse between the lines

x = \frac{1}{2}

and

x = 1

\frac{1}{16} (π - 2)

View solution

Question 3

The axis of a parabola is along the line

y = x

and the distance of its vertex and focus from the origin are

2

and

22

, respectively. If vertex and focus both lie in the first quadrant, then the equation of the parabola is

(x + y)^{2} = (x - y - 2)

(x - y)^{2} = (x + y - 2)

(x - y)^{2} = 4 (x + y - 2)

(x - y)^{2} = 8 (x + y - 2)

View solution

Question 4

The normal at a point

P

on the ellipse

x^{2} + 4 y^{2} = 16

meets the x-axis at

Q ˙

M

is the midpoint of the line segment

P Q,

then the locus of

M

intersects the latus rectums of the given ellipse at points. (a)

(\pm \frac{( 3 5 )}{2} \pm \frac{2}{7})

(b)

(\pm \frac{( 3 5 )}{2} \pm \frac{19}{7})

(c)

(\pm 23, \pm \frac{1}{7})

(d)

(\pm 23 \pm \frac{4 3}{7})

View solution

Question Text

Find the length of the common chord of the circles

x^{2} + y^{2} + 2 x + 6 y = 0

and

x^{2} + y^{2} - 4 x - 2 y - 6 = 0

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Find the length of the common chord of the circles x2+y2+2x+6y=0 and x2+y2−4x−2y−6=0

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Practice questions from similar books

Find the length of the common chord of the circles $x^{2} + y^{2} + 2 x + 6 y = 0$ and $x^{2} + y^{2} - 4 x - 2 y - 6 = 0$