The line passes through the centre of circle \(x^2 + y^2 – 16x – 4y = 0\), it interacts with the positive coordinate axis at A & B. Then find the minimum value of OA + OB, where O is origin.
- 20
- 18
- 12
- 24
The Correct Option is A
Solution and Explanation
Top Questions on general equation of a line
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Questions Asked in JEE Main exam
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A force \( \vec{f} = x^2 \hat{i} + y \hat{j} + y^2 \hat{k} \) acts on a particle in a plane \( x + y = 10 \). The work done by this force during a displacement from \( (0,0) \) to \( (4m, 2m) \) is Joules (round off to the nearest integer).
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- Consider a long thin conducting wire carrying a uniform current \( I \). A particle having mass \( M \) and charge \( q \) is released at a distance \( a \) from the wire with a speed \( v_0 \) along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance \( x \) from the wire. The value of \( x \) is:
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Concepts Used:
General Equation of a Line
Equation of Straight Line Formula:
A straight line is a figure created when two points A (x1, y1) and B (x2, y2) are connected with a minimum distance between them, and both the ends are extended to immensity (infinity). With variables x and y, the standard form of a linear equation is: ax + by = c, where a, b, and c are constants and x, and y are variables.
Point Slope Form:
The equation of a straight line whose slope is m and passes through a point (x1, y1) is formed or created using the point-slope form. The equation of the point-slope form is:
y - y1 = m (x - x1),
where (x, y) = an arbitrary point on the line.