Home
Class 12
MATHS
Let C be the circle of unit radius centr...

Let C be the circle of unit radius centred at the origin. If two positive numbers `x_(1)` and `x_(2)` are such that the line passing through `(x_(1),-1)` and `(x_(2),1)` is tangent to C then

A

`x_(1)x_(2)=1`

B

`x_(1)x_(2)=-1`

C

`x_(1)+x_(2)=1`

D

`4x_(1)x_(2)=1 `

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise - 2 : One or More than One Answer is/are Correct|10 Videos

  • CIRCLE

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise - 3 : Comprehension Type Problems|8 Videos

  • BIONMIAL THEOREM

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|15 Videos

  • COMPLEX NUMBERS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE-5 : SUBJECTIVE TYPE PROBLEMS|8 Videos

Similar Questions

Explore conceptually related problems

Let C be the circle of radius unity centred at the origin. If two positive numbers x_1 and x_2 are such that the line passing through (x_1,-1) and (x_2, 1) is tangent to C then x_1*x_2

Circle will centre origin and passing through (-1,2) is

Circle with centre (-1,2) and passing through origin is

The equation of the circle with radius 3 units, passing through the point (2, 1) and whose centre lies on the line y + x = 0 can be

The radical centre of the three circles is at the origin. The equations of the two of the circles are x^(2)+y^(2)=1 and x^(2)+y^(2)+4x+4y-1=0 . If the third circle passes through the points (1, 1) and (-2, 1), and its radius can be expressed in the form of (p)/(q) , where p and q are relatively prime positive integers. Find the value of (p+q) .

The centres of two circles C_(1) and C_(2) each of unit radius are at a distance of 6 unit from each other. Let P be the mid-point of the line segment joining the centres of C_(1) and C_(2) and C be a circle touching circles C_(1) and C_(2) externally. If a common tangent to C_(1) and C passing through P is also a common tangent to C_(2) and C, then the radius of the circle C, is

The centres of two circles C_(1) and C_(2) each of unit radius are at a distance of 6 unit from each other. Let P be the mid-point of the line segment joining the centres of C_(1) and C_(2) and C be a circle touching circles C_(1) and C_(2) externally. If a common tangent to C_(1) and C passing through P is also a common tangent to C_(2) and C, then the radius of the circle C, is

C_1 and C_2 are circle of unit radius with centers at (0, 0) and (1, 0), respectively, C_3 is a circle of unit radius. It passes through the centers of the circles C_1a n dC_2 and has its center above the x-axis. Find the equation of the common tangent to C_1a n dC_3 which does not pass through C_2dot

Let C be the centroid of the triangle with vertices (3, -1) (1, 3) and ( 2, 4). Let P be the point of intersection of the lines x+3y-1=0 and 3x-y+1=0 . Then the line passing through the points C and P also passes through the point :

A circle of radius 1 unit touches the positive x-axis and the positive y-axis at A and B , respectively. A variable line passing through the origin intersects the circle at two points D and E . If the area of triangle D E B is maximum when the slope of the line is m , then find the value of m^(-2)