Advertisements
Advertisements
Question
Answer the following :
Find the equation of tangent to Circle x2 + y2 – 6x – 4y = 0, at the point (6, 4) on it
Solution 1
Given equation of the circle is
x2 + y2 – 6x – 4y = 0
Comparing this equation with
x2 + y2 + 2gx + 2fy + c = 0, we get
2g = –6, 2f = –4, c = 0
∴ g = –3, f = –2, c = 0
The equation of a tangent to the circle
x2 + y2 + 2gx + 2fy + c = 0 at (x1, y1) is
xx1 + yy1 + g(x + x1) + f(y + y1) + c = 0
∴ the equation of the tangent at (6, 4) is
x(6) + y(4) – 3(x + 6) – 2(y + 4) + 0 = 0
∴ 6x + 4y – 3x – 18 – 2y – 8 = 0
∴ 3x + 2y – 26 = 0
Solution 2
Given equation of the circle is
x2 + y2 – 6x – 4y = 0
∴ x(x – 6) + y(y – 4) = 0, which is in diameter form where (0, 0) and (6, 4) are endpoints of diameter.
Slope of OP = `(4 - 0)/(6 - 0) = 2/3`
Since, OP is perpendicular to the required tangent.
∴ Slope of the required tangent = `(-3)/2`
∴ the equation of the tangent at (6, 4) is
y – 4 = `(-3)/2(x - 6)`
∴ 2(y – 4) = –3(x – 6)
∴ 2y – 8 = –3x + 18
∴ 3x + 2y – 26 = 0
APPEARS IN
RELATED QUESTIONS
Find the equation of a tangent to the circle x2 + y2 − 3x + 2y = 0 at the origin
Show that the line 7x − 3y − 1 = 0 touches the circle x2 + y2 + 5x − 7y + 4 = 0 at point (1, 2)
Find the equation of tangent to the circle x2 + y2 − 4x + 3y + 2 = 0 at the point (4, −2)
Choose the correct alternative:
The equation of the tangent to the circle x2 + y2 = 4 which are parallel to x + 2y + 3 = 0 are
Choose the correct alternative:
A pair of tangents are drawn to a unit circle with center at the origin and these tangents intersect at A enclosing an angle of 60°. The area enclosed by these tangents and the area of the circle is
Answer the following :
Find the equation of tangent to the circle x2 + y2 = 64 at the point `"P"((2pi)/3)`
Answer the following :
Find the value of k, if the length of the tangent segment from the point (8, –3) to the circle
x2 + y2 – 2x + ky – 23 = 0 is `sqrt(10)`
Answer the following :
Find the equation of tangent to Circle x2 + y2 = 5, at the point (1, –2) on it
Answer the following :
Find the equation of the tangent to Circle x = 5 cosθ. y = 5 sinθ, at the point θ = `pi/3` on it
Answer the following :
Show that 2x + y + 6 = 0 is a tangent to x2 + y2 + 2x – 2y – 3 = 0. Find its point of contact
Answer the following :
If the tangent at (3, –4) to the circle x2 + y2 = 25 touches the circle x2 + y2 + 8x – 4y + c = 0, find c
Answer the following :
Find the equations of the tangents to the circle x2 + y2 = 36 which are perpendicular to the line 5x + y = 2
Answer the following :
Find the equations of the tangents to the circle x2 + y2 – 2x + 8y – 23 = 0 having slope 3
Answer the following :
Find the equation of the locus of a point, the tangents from which to the circle x2 + y2 = 9 are at right angles.
Answer the following :
Tangents to the circle x2 + y2 = a2 with inclinations, θ1 and θ2 intersect in P. Find the locus of such that cot θ1 + cot θ2 = 5
Answer the following :
Tangents to the circle x2 + y2 = a2 with inclinations, θ1 and θ2 intersect in P. Find the locus of such that cot θ1 . cot θ2 = c
The abscissae of the points, where the tangent to curve `y = x^3 - 3/2x^2 - 6x + 7/5` is parallel to X-axis, are ______
The equation of the tangent to the curve y = `2x + 1/x^2`, that is parallel to the X-axis, is ______.
The number of common tangents to the circles x2 + y2 - x = 0 and x2 + y2 + x = 0 is ______
