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प्रश्न
Find the length of the tangent from (1, 2) to the circle x2 + y2 – 2x + 4y + 9 = 0.
उत्तर
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
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संबंधित प्रश्न
Find the centre and radius of the circle
x2 + y2 = 16
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.
Find the equation of the tangent to the circle x2 + y2 – 4x + 4y – 8 = 0 at (-2, -2).
Determine whether the points P(1, 0), Q(2, 1) and R(2, 3) lie outside the circle, on the circle or inside the circle x2 + y2 – 4x – 6y + 9 = 0.
If (4, 1) is one extremity of a diameter of the circle x2 + y2 - 2x + 6y - 15 = 0 find the other extremity.
The equation of the circle with centre on the x axis and passing through the origin is:
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Find centre and radius of the following circles
x2 + y2 + 6x – 4y + 4 = 0
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 equation of the normal to the circle x2 + y2 – 2x – 2y + 1 = 0 which is parallel to the line 2x + 4y = 3 is
