Advertisements
Advertisements
Question
Find the length of the tangent from (1, 2) to the circle x2 + y2 – 2x + 4y + 9 = 0.
Solution
The length of the tangent from (x1, y1) to the circle x2 + y2 – 2x + 4y + 9 = 0 is `sqrt(x_1^2 + y_1^2 - 2x_1 + 4y_1 + 9)`
Length of the tangent from (1, 2) = `sqrt(1^2 + 2^2 - 2(1) + 4(2) + 9)`
`= sqrt(1 + 4 - 2 + 8 + 9)`
`= sqrt20`
`= sqrt(4 xx 5)`
`= 2sqrt5` units
APPEARS IN
RELATED QUESTIONS
Find the centre and radius of the circle
x2 + y2 – 22x – 4y + 25 = 0
Find the equation of the circle passing through the points (0, 1), (4, 3) and (1, -1).
Find the equation of the circle on the line joining the points (1, 0), (0, 1), and having its centre on the line x + y = 1.
If the lines x + y = 6 and x + 2y = 4 are diameters of the circle, and the circle passes through the point (2, 6) then find its equation.
Find the value of P if the line 3x + 4y – P = 0 is a tangent to the circle x2 + y2 = 16.
If the circle touches the x-axis, y-axis, and the line x = 6 then the length of the diameter of the circle is:
Find the equation of circles that touch both the axes and pass through (− 4, −2) in general form
Choose the correct alternative:
The equation of the circle passing through (1, 5) and (4, 1) and touching y-axis `x^2 + y^2 - 5x - 6y + 9 + lambda(4x + 3y - 19)` = where `lambda` is equal to
Choose the correct alternative:
The length of the diameter of the circle which touches the x -axis at the point (1, 0) and passes through the point (2, 3)
Choose the correct alternative:
The radius of the circle passing through the points (6, 2) two of whose diameter are x + y = 6 and x + 2y = 4 is
