The acute angle between the line 3x-4y=5...

The acute angle between the line `3x-4y=5` and the circle `x^2+y^2-4x+2y-4=0` is `theta` . Then find the value of `9costheta`.

Text Solution

AI Generated Solution

Topper's Solved these Questions

COMPLEX NUMBERS AND QUADRATIC EQUATIONS
CENGAGE ENGLISH|Exercise All Questions|886 Videos
DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS
CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

The acute angle between the line 3x-4y=5 and the circle x^2+y^2-4x+2y-4=0 is theta . Then 9costheta=

Find the acute angle between the lines 2x-y+3=0\ a n d\ x+y+2=0.

If the angle between the two lines represented by 2x^2+5x y+3y^2+6x+7y+4=0 is tan^(-1)(m), then find the value of mdot

The angle between the circles x^2+y^2-2x-4y+3=0 and x^2+y^2-4x-6y+11=0 is

If the angle between the two lines represented by 2x^2+5x y+3y^2+6x+7y+4=0 is tan^(-1)(m), then find the value of m .

If the line 3x+4y=k is tangent to the circle x^2+y^2-2x-4y+4=0 , then number of integral values of k is

If theta is the angle between the lines given by the equation 6x^2+5x y-4y^2+7x+13 y-3=0 , then find the equation of the line passing through the point of intersection of these lines and making an angle theta with the positive x-axis.

Find the image of the circle x^2+y^2-2x+4y-4=0 in the line 2x-3y+5=0

The line 3x -4y = k will cut the circle x^(2) + y^(2) -4x -8y -5 = 0 at distinct points if

CENGAGE ENGLISH-CONIC SECTIONS-All Questions

Line segments A C and B D are diameters of the circle of radius 1. If ...
Text Solution
|
As shown in the figure, three circles which have the same radius r,hav...
Text Solution
|
The acute angle between the line 3x-4y=5 and the circle x^2+y^2-4x+2y-...
Text Solution
|
If two perpendicular tangents can be drawn from the origin to the c...
Text Solution
|
Let A(−4,0), B(4,0) & C(x,y) be points on the circle x^2 + y^2 = 16 su...
Text Solution
|
If the circle x^2 + y^2 + ( 3 + sin beta) x + 2 cos alpha y = 0 and x...
Text Solution
|
A tangent at a point on the circle x^2+y^2=a^2 intersects a concentric...
Text Solution
|
Tangent are drawn to the circle x^2+y^2=1 at the points where it is me...
Text Solution
|
From the points (3, 4), chords are drawn to the circle x^2+y^2-4x=0 ....
Text Solution
|
The angles at which the circles (x-1)^2+y^2=10a n dx^2+(y-2)^2=5 inte...
Text Solution
|
Two circles of radii 4cm and 1cm touch each other externally and theta...
Text Solution
|
The locus of the midpoints of the chords of the circle x^2+y^2-a x-b y...
Text Solution
|
A is a point (a, b) in the first quadrant. If the two circIes which pa...
Text Solution
|
The number of common tangent(s) to the circles x^2+y^2+2x+8y-23=0 and ...
Text Solution
|
If the tangents are drawn from any point on the line x+y=3 to the circ...
Text Solution
|
If the radius of the circumcircle of the triangle TPQ, where PQ is ch...
Text Solution
|
If the radius of the circumcircle of the triangle TPQ, where PQ is ch...
Text Solution
|
The equation of the locus of the middle point of a chord of the circle...
Text Solution
|
Two circles C1a n dC2 intersect at two distinct points Pa n dQ in a li...
Text Solution
|
The two points A and B in a plane are such that for all points P lies ...
Text Solution
|