Advertisements
Advertisements
प्रश्न
Find the value of P if the line 3x + 4y – P = 0 is a tangent to the circle x2 + y2 = 16.
उत्तर
The condition for a line y = mx + c to be a tangent to the circle x2 + y2 = a2 is c2 = a2 (1 + m2)
Equation of the line is 3x + 4y – P = 0
Equation of the circle is x2 + y2 = 16
4y = -3x + P
y = `(-3)/4x + "P"/4`
∴ m = `(-3)/4`, c = `"P"/4`
Equation of the circle is x2 + y2 = 16
∴ a2 = 16
Condition for tangency we have c2 = a2(1 + m2)
⇒ `("P"/4)^2 = 16 (1 + 9/16)`
⇒ `"P"^2/16 = 16(25/16)`
⇒ P2 = 16 × 25
⇒ P = ± `sqrt16 xx sqrt25`
⇒ P = ±4 × 5
⇒ P = ±20
APPEARS IN
संबंधित प्रश्न
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 values of a and b if the equation (a - 1)x2 + by2 + (b - 8)xy + 4x + 4y - 1 = 0 represents a circle.
In the equation of the circle x2 + y2 = 16 then v intercept is (are):
If the perimeter of the circle is 8π units and centre is (2, 2) then the equation of the circle is:
Find the equation of circles that touch both the axes and pass through (− 4, −2) in general form
Find the equation of the circles with centre (2, 3) and passing through the intersection of the lines 3x – 2y – 1 = 0 and 4x + y – 27 = 0
If y = `2sqrt(2)x + "c"` is a tangent to the circle x2 + y2 = 16, find the value of c
Find centre and radius of the following circles
x2 + y2 + 6x – 4y + 4 = 0
Choose the correct alternative:
The radius of the circle 3x2 + by2 + 4bx – 6by + b2 = 0 is
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
