Home
Class 12
MATHS
The length of the diameter of the circle...

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)

A

`(10)/(3)`

B

`(3)/(5)`

C

`(6)/(5)`

D

`(5)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A

Circle touches x-axis at (1,0).
So, center of circle is `(1,k)` and radius is k.
Hence , equation of circle is `:`
`(x-1)^(2)+(y-k)^(2)=k^(2)`
It passes through the point (2,3), so
`(2-1)^(2)+(3-k)^(2)=k^(2)`
`:. 1+9-6k+k^(2)=k^(2)`
`:. k = 5//3`
`:. ` diameter `=2k = 10//3`
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    CENGAGE ENGLISH|Exercise JEE ADVANCED (Single Correct Answer Type)|3 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise LINKED COMPREHENSION TYPE (For problem 1 and 2)|2 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise ARCHIVES (JEE MAIN)|1 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Matrix|4 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

Similar Questions

Explore conceptually related problems

A circle having its centre in the first quadrant touches the y-axis at the point (0,2) and passes through the point (1,0). Find the equation of the circle

Equation of the smaller circle that touches the circle x^2+y^2=1 and passes through the point (4,3) is

Find the equation of the circle with radius 5 whose center lies on the x-axis and passes through the point (2, 3).

Find the length of the diameter of the cirlce which passes through the points (-3, 6), (-5, 2) and (3, -6) .

Determine the quadratic curve y=f(x) if it touches the line y=x at the point x=1 and passes through the point (-1,0) .

Determine the quadratic curve y=f(x) if it touches the line y=x at the point x=1 and passes through the point (-1,\ 0) .

The equation of radical axis of two circles is x + y = 1 . One of the circles has the ends ofa diameter at the points (1, -3) and (4, 1) and the other passes through the point (1, 2).Find the equations of these circles.

Find the equation of the circle which passes through the points (0,0), (0,1) and (2,3)

The circle passing through (1, -2) and touching the axis of x at (3, 0) also passes through the point

A ray of light passing through the point (1, 2) reflects on the x–axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.