Home
Class 12
MATHS
Tangents are drawn to x^(2)+y^(2)=1 from...

Tangents are drawn to `x^(2)+y^(2)=1` from any arbitrary point P on the line `2x+y-4=0`.Prove that corresponding chords of contact pass through a fixed point and find that point.

Text Solution

AI Generated Solution

To solve the problem, we need to show that the chords of contact from any point \( P \) on the line \( 2x + y - 4 = 0 \) to the circle \( x^2 + y^2 = 1 \) pass through a fixed point. We will find this fixed point step by step. ### Step 1: Identify the Circle and the Line The equation of the circle is given by: \[ x^2 + y^2 = 1 \] The equation of the line is: ...
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    CENGAGE ENGLISH|Exercise Examples|13 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 4.1|1 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Matrix|4 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

Similar Questions

Explore conceptually related problems

Tangents are drawn to x^2+y^2=1 from any arbitrary point P on the line 2x+y-4=0 . The corresponding chord of contact passes through a fixed point whose coordinates are(a) (1/2,1/2) (b) (1/2,1) (c) (1/2,1/4) (d) (1,1/2)

Tangents PA and PB are drawn to the circle x^2 +y^2=8 from any arbitrary point P on the line x+y =4 . The locus of mid-point of chord of contact AB is

Tangents are drawn from the points on the line x-y-5=0 to x^2+4y^2=4 . Then all the chords of contact pass through a fixed point. Find the coordinates.

Tangents PA and PB are drawn to parabola y^(2)=4x from any arbitrary point P on the line x+y=1 . Then vertex of locus of midpoint of chord AB is

From a variable point p on line 2x−y-1=0 pair of tangents are drawn to parabola x^2=8y then chord of contact passes through a fixed point.

Tangents are drawn from the points on the line x−y−5=0 to x^2+4y^2=4 , then all the chords of contact pass through a fixed point, whose coordinate are

Tangent is drawn at any point (p ,q) on the parabola y^2=4a x .Tangents are drawn from any point on this tangant to the circle x^2+y^2=a^2 , such that the chords of contact pass through a fixed point (r , s) . Then p ,q ,r and s can hold the relation (A) r^2q=4p^2s (B) r q^2=4p s^2 (C) r q^2=-4p s^2 (D) r^2q=-4p^2s

Tangents are drawn to the hyperbola x^(2)-y^(2)=3 which are parallel to the line 2x+y+8=0 . Then their points of contact is/are :

Tangent is drawn at any point (x_1,y_1) on the parabola y^2=4ax . Now tangents are drawn from any point on this tangent to the circle x^2+y^2=a^2 such that all the chords of contact pass throught a fixed point (x_2,y_2) Prove that 4(x_1/x_2)+(y_1/y_2)^2=0 .

Tangent is drawn at any point (x_1, y_1) other than the vertex on the parabola y^2=4a x . If tangents are drawn from any point on this tangent to the circle x^2+y^2=a^2 such that all the chords of contact pass through a fixed point (x_2,y_2), then (a) x_1, a ,x_2 in GP (b) (y_1)/2,a ,y_2 are in GP (c) -4,(y_1)/(y_2),x_1/x_2 are in GP (d) x_1x_2+y_1y_2=a^2