Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20209 JanuaryMorning Shift
Exam
JEE Main
Year
2020
Date
9 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Circle

JEE Main 2020 · 9 January · Morning Shift · Mathematics · Circle

A circle touches the y-axis at the point (0, 4) and passes through...

A circle touches the y-axis at the point (0,4)\left(0, 4\right) and passes through the point (2,0)\left(2, 0\right) . 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

Options

  1. A4x−3y+17=04x - 3y + 17 = 0
  2. B3x−4y−24=03x - 4y - 24 = 0
  3. C3x+4y−6=03x + 4y - 6 = 0
  4. D4x+3y−8=04x + 3y - 8 = 0

Correct answer

D. 4x+3y−8=04x + 3y - 8 = 0

Step-by-step solution

A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0) . Which of the following lines is
Equation of family of circle
(x−0){\left(x - 0\right)}^{2} + {\left(y - 4\right)}^{2} + \lambdax = 0 ⇒ passes\left(2, 0\right)<br/><br/>4 + 16 + 2\lambda = 0 ⇒ \lambda = - 10<br/><br/>{x}^{2} + {y}^{2} - 10x - 8y + 16 = 0<br/>Centre(5,4),R=25+16−16=5<br/>Centre \left(5,4\right), R = \sqrt{25 + 16 - 16} = 5
Check the options.
Option (4)
\left|\dfrac{4 \times 5 + 3 \times 4 - 8}{5}\right| = \dfrac{24}{5} \ne 5
Practice Circle on Quantrex Academy →

More from Circle

Match each entry in List-I to the correct entry in List-II and choose the correct option.… JEE Advanced 2026Consider the circle C: x^2+y^2-6x-8y-11=0 . Let a variable chord AB of the circle C… JEE Main 2026Let C be a circle having centre in the first quadrant and touching the x -axis at a… JEE Main 2026Let the line x - y = 4 intersect the circle C: (x-4)^2 + (y+3)^2 = 9 at the points Q and… JEE Main 2026Let the centre of the circle x^2 + y^2 + 2gx + 2fy + 25 = 0 be in the first quadrant and… JEE Main 2026Let P be a moving point on the circle x^2 + y^2 - 6x - 8y + 21 = 0 . Then, the maximum… JEE Main 2026Suppose that two chords, drawn from the point (1, 2) on the circle x^2 + y^2 + x - 3y = 0… JEE Main 2026Let a circle pass through the origin and its centre be the point of intersection of two… JEE Main 2026Let a circle C have its centre in the first quadrant, intersect the coordinate axes at… JEE Main 2026Let the circle x^ 2 +y^ 2 =4 intersect x -axis at the points A(a, 0), a>0 and B(b, 0) .… JEE Main 2026Let y=x be the equation of a chord of the circle C_ 1 (in the closed half-plane x ≥ 0 )… JEE Main 2026Let S=\ z ∈ ℂ:|(z-6 i)/(z-2 i)|=1. and .|(z-8+2 i)/(z+2 i)|=(3)/(5)\ . Then ∑_ z ∈ ~s… JEE Main 2026Let a circle of radius 4 pass through the origin O, the points A(- 3 a, 0) and B(0,- 2 b)… JEE Main 2026If the points of intersection of the ellipses x^ 2 +2 y^ 2 -6 x-12 y+23=0 and 4 x^ 2 +2… JEE Main 2026Let the set of all values of r , for which the circles (x+1)^ 2 +(y+4)^ 2 =r^ 2 and x^ 2… JEE Main 2026If P is a point on the circle x^ 2 +y^ 2 =4, Q is a point on the straight line 5 x+y+2=0… JEE Main 2026 Full Circle list Circle JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs