Intercepts Made by a Circle

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JEE Advanced 1999

Let $L_{1}$ be a straight line passing through the origin and $L_{2}$ be the straight line $x + y = 1$ . If the intercepts made by the circle $x^{2} + y^{2} - x + 3 y = 0$ on $L_{1}$ and $L_{2}$ are equal, then which of the following equations can represent $L_{1}$ ?

x + y = 0

(B)

x - y = 0

(C)

x + 7 y = 0

(D)

x - 7 y = 0

JEE Advanced 1991

LEVELJEE Main

If a circle passes through the points of intersection of the coordinate axes with the lines $λ x - y + 1 = 0$ and $x - 2 y + 3 = 0$ , then the value of $λ = .........$

JEE Main 2019 (8 April Shift 1)

LEVELJEE Main

The sum of the squares of the lengths of the chords intercepted on the circle, $x^{2} + y^{2} = 16$ , by the lines, $x + y = n, n \in N$ , where $N$ is the set of all natural numbers, is :

(A)

320

(B)

160

(C)

105

(D)

210

JEE Main 2020 - 5 Sep (Evening)

LEVELJEE Main

If the length of the chord of the circle, $x^{2} + y^{2} = r^{2} (r > 0)$ along the line, $y - 2 x = 3$ is $r$ then $r^{2}$ is equal to :

(A)

\frac{9}{24}

(B)

\frac{24}{5}

(C)

\frac{12}{5}

(D)

12

JEE Main 2021 (27 July Shift 2)

LEVELJEE Main

Consider a circle $C$ which touches the $y$ -axis at $(0, 6)$ and cuts off an intercept $65$ on the $x$ -axis. Then the radius of the circle $C$ is equal to :

(A)

53

(B)

(C)

(D)

82

JEE Main 2022 (27 July Shift 1)

LEVELJEE Main

If the circle $x^{2} + y^{2} - 2 g x + 6 y - 19 c = 0, g, c \in R$ passes through the point $(6, 1)$ and its centre lies on the line $x - 2 cy = 8$ , then the length of intercept made by the circle on x-axis is

(A)

11

(B)

(C)

(D)

223

JEE Main 2023 (12 April Shift 1)

LEVELJEE Main

Two circles in the first quadrant of radii $r_{1}$ and $r_{2}$ touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line $x + y = 2$ . Then $r_{1}^{2} + r_{2}^{2} - r_{1} r_{2}$ is equal to ____.

JEE(ADVANCED)-201

LEVELJEE Main

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If a circle passes through the points of intersection of the coordinate axes with the lines λx−y+1=0 and x−2y+3=0, then the value of λ=.........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The sum of the squares of the lengths of the chords intercepted on the circle, x2+y2=16, by the lines, x+y=n,n∈N, where N is the set of all natural numbers, is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the length of the chord of the circle, x2+y2=r2(r>0) along the line, y−2x=3 is r then r2 is equal to :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Consider a circle C which touches the y-axis at (0,6) and cuts off an intercept 65​ on the x-axis. Then the radius of the circle C is equal to :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For how many values of p, the circle x2+y2+2x+4y−p=0 and the coordinate axes have exactly three common points ?

If a circle passes through the points of intersection of the coordinate axes with the lines $λ x - y + 1 = 0$ and $x - 2 y + 3 = 0$ , then the value of $λ = .........$

The sum of the squares of the lengths of the chords intercepted on the circle, $x^{2} + y^{2} = 16$ , by the lines, $x + y = n, n \in N$ , where $N$ is the set of all natural numbers, is :

If the length of the chord of the circle, $x^{2} + y^{2} = r^{2} (r > 0)$ along the line, $y - 2 x = 3$ is $r$ then $r^{2}$ is equal to :

Consider a circle $C$ which touches the $y$ -axis at $(0, 6)$ and cuts off an intercept $65$ on the $x$ -axis. Then the radius of the circle $C$ is equal to :

For how many values of $p$ , the circle $x^{2} + y^{2} + 2 x + 4 y - p = 0$ and the coordinate axes have exactly three common points ?