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NDA Circles questions with solutions

Equations and properties of circles. 21 questions from our 2016–2025 NDA pattern papers, from the Class 11 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Circles for CAT

NDA 2025

The equation of the circle which is concentric with x^2+y^2-4x+6y-3=0 and passes through the point (1,1) isNDA 2025 Maths · medium
The circle x^2+y^2-4x-6y+9=0 touchesNDA 2025 Maths · medium

NDA 2024

The equation of the circle having the points (1,2) and (7,10) as the end points of a diameter isNDA 2024 Maths · medium
The shortest distance of the point (9,12) from the circle x^2+y^2=16 isNDA 2024 Maths · hard
The equation of the circle concentric with x^2+y^2-4x+2y-7=0 and passing through the point (1,1) isNDA 2024 Maths · medium

NDA 2023

The line y=mx+4 touches the circle x^2+y^2=8. The possible values of m areNDA 2023 Maths · medium
The line 3x+4y=15 cuts the circle x^2+y^2=25 in a chord of lengthNDA 2023 Maths · medium

NDA 2022

The circles x^2+y^2=9 and x^2+y^2-8x-6y+k=0 intersect orthogonally.NDA 2022 Maths · hard

NDA 2021

The length of the chord intercepted on the x-axis by the circle (x-3)^2+(y-4)^2=25 isNDA 2021 Maths · medium
The number of common tangents to the circles x^2+y^2=1 and (x-5)^2+y^2=4 isNDA 2021 Maths · hard
The line 3x+4y=25 cuts the circle x^2+y^2=25 at two distinct points. 2. x^2+y^2+2x+2y+5=0 represents a real circle.NDA 2021 Maths · hard

NDA 2020

The equation of the circle with centre (-2,3) that touches the x-axis isNDA 2020 Maths · easy
The circles x^2+y^2=4 and (x-3)^2+y^2=1 have exactly how many common tangents?NDA 2020 Maths · medium
The circle passing through the origin and the points (4,0) and (0,6) has radiusNDA 2020 Maths · hard

NDA 2019

A circle of radius 5 lies in the first quadrant and touches the y-axis at the point (0,3). Its centre isNDA 2019 Maths · easy
The circles x^2+y^2=16 and x^2+y^2-6x-8y+9=0 have exactly how many common tangents?NDA 2019 Maths · hard
The length of the chord cut off from the circle x^2+y^2=25 by the line 3x+4y=15 isNDA 2019 Maths · medium
A tangent to a circle is perpendicular to the radius drawn to its point of contact. 2. The line y=x+3 touches the circle x^2+y^2=9.NDA 2019 Maths · medium

NDA 2017

The equation of the circle having the points (1,2) and (5,4) as ends of a diameter isNDA 2017 Maths · medium
The line y=2x passes through the centre of the circle x^2+y^2-2x-4y+1=0. 2. The origin lies inside the circle x^2+y^2-6x-8y+9=0.NDA 2017 Maths · medium

NDA 2016

The circles x^2+y^2=4 and (x-3)^2+y^2=1 touch each other externally. 2. The line y=x+3 is a tangent to the circle x^2+y^2=9.NDA 2016 Maths · medium