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Class 12 Maths Practice Test - Tangents and Normals
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Class 12 Maths Practice Test - Tangents and Normals
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25 Questions

1. What will be the length of a tangent from the point (7, 2) to the circle 2x2 + 2y2 + 5 x + y = 15?
2. Find the equation of all the lines having slope 0 which are tangent to the curve y=6x2-7x.
3. What will be the equation of the normal to the parabola y2 = 3x which is perpendicular to the line y = 2x + 4?
4. What will be the equation of the normal to the hyperbola xy = 4 at the point (2, 2)?
5. If the curves x2/a + y2/b = 1 and x2/c + y2/d = 1 intersect at right angles, then which one is the correct relation?
6. Find the tangent to the curve y=3x2+x+4 at x=3.
7. What will be the equation of the tangent to the circle x2 + y2 – 6x + 4y – 7 = 0, which are perpendicular to the straight line 2x – y + 3 = 0?
8. At which point does the normal to the hyperbola xy = 4 at (2, 2) intersects the hyperbola again?
9. What is the equation of the tangent at a specific point of y2 = 4ax at (0, 0)?
10. What is the equation of the tangent at a specific point of y2 = 4ax at (0, 0)?
11. Find the points on the curve y=3x4+2x3-1 at which the tangents is parallel to the x-axis.
12. Find the point at which the tangent to the curve y=\(\sqrt{4x^2+1}\)-2 has its slope2.
13. If X and Y are given as current co-ordinates, what is the equation of the tangent at a specific point of x3 – 3axy + y3 = 0 at (x, y)?
14. Find the tangent to the curve y=7x3-2x2 at the point x=2.
15. What will be the co-ordinates of the foot of the normal to the parabola y2 = 5x that makes an angle 45° with the x axis?
16. What will be the co-ordinates of the foot of the normal to the parabola y2 = 3x which is perpendicular to the line y = 2x + 4?
17. If the normal to the ellipse x2 + 3y2 = 12 at the point be inclined at 60° to the major axis, then at what angle does the line joining the curve to the point is inclined to the same axis?
18. Find the equation of the normal to the curve x=12 cosec⁡θ and y=2 sec⁡θ at x=π/4 .
19. What will be the equation of the tangent to the circle x2 + y2 – 6x + 4y – 7 = 0, which are perpendicular to the straight line 2x – y + 3 = 0?
20. What will be the equation of the normal to the parabola y2 = 5x that makes an angle 45° with the x axis?
21. What will be the value of angle between the curves x2 – y2 = 2a2 and xv + y2 = 4a2?
22. Find the tangent to the curve y=5x4-3x2+2x-1 at x=1.
23. What is the nature of the straight line x + y + 7 = 0 to the hyperbola 3x2 – 4y2 = 12 whose normal is at the point (x1, y1)?
24. Find the slope of the tangent to the curve x=4 cos3⁡3θ and y=5 sin3⁡⁡3θ at θ=π/4.
25. What will be the equation of the circle which touches the line x + 2y + 5 = 0 and passes through the point of intersection of the circle x2 + y2 = 1 and x2 + y2 + 2x + 4y + 1 = 0?

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