A circle touches the $y$ -axis at the point $(0,4)$ and passes through the point $(2,0) .$ Which of the following lines is not a tangent to this circle?
A circle touches the $y$ -axis at the point $(0,4)$ and passes through the point $(2,0) .$ Which of the following lines is not a tangent to this circle?
- [JEE MAIN 2020]
- A
$3 x-4 y-24=0$
- B
$3 x+4 y-6=0$
- C
$4 x+3 y-8=0$
- D
$4 x-3 y+17=0$
Similar Questions
Tangents drawn from origin to the circle ${x^2} + {y^2} - 2ax - 2by + {b^2} = 0$ are perpendicular to each other, if
Tangents drawn from origin to the circle ${x^2} + {y^2} - 2ax - 2by + {b^2} = 0$ are perpendicular to each other, if
The equation of the tangents to the circle ${x^2} + {y^2} + 4x - 4y + 4 = 0$ which make equal intercepts on the positive coordinate axes is given by
The equation of the tangents to the circle ${x^2} + {y^2} + 4x - 4y + 4 = 0$ which make equal intercepts on the positive coordinate axes is given by
Match the statements in Column $I$ with the properties Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
Column $I$
Column $II$
$(A)$ Two intersecting circles
$(p)$ have a common tangent
$(B)$ Two mutually external circles
$(q)$ have a common normal
$(C)$ two circles, one strictly inside the other
$(r)$ do not have a common tangent
$(D)$ two branches of a hyperbola
$(s)$ do not have a common normal
Match the statements in Column $I$ with the properties Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
| Column $I$ | Column $II$ |
| $(A)$ Two intersecting circles | $(p)$ have a common tangent |
| $(B)$ Two mutually external circles | $(q)$ have a common normal |
| $(C)$ two circles, one strictly inside the other | $(r)$ do not have a common tangent |
| $(D)$ two branches of a hyperbola | $(s)$ do not have a common normal |
- [IIT 2007]
The area of the triangle formed by the positive $x$-axis and the normal and the tangent to the circle $x^2 + y^2 = 4$ at $(1, \sqrt 3 )$ is
The area of the triangle formed by the positive $x$-axis and the normal and the tangent to the circle $x^2 + y^2 = 4$ at $(1, \sqrt 3 )$ is
A pair of tangents are drawn from the origin to the circle ${x^2} + {y^2} + 20(x + y) + 20 = 0$. The equation of the pair of tangents is
A pair of tangents are drawn from the origin to the circle ${x^2} + {y^2} + 20(x + y) + 20 = 0$. The equation of the pair of tangents is