TN Maths, 12th Chapter 5 Important Questions

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Class : XII

Subject : Maths

Chapter : 5

Chapter : Two Dimentional Analytical Geometry - II

IMPORTANT QUESTIONS

      

2 & 3 Marks Questions

1. Find the general equation of a circle with centre (-3,4) and radius 3 units .

2. A circle of radius 3 units touches both the axes. Find the equations of all possible circles formed in the general form.

3. Find the equations of the tangent and normal to the circle x²+y² = 25 at p(-3,4).

4. If y= 4x+c is a tangent to the circle x²+y²= 9, find c.

5. Obtain the equation of the circles with radius 5 cm and touching x-axis at the origin in general form.

6.If y= 2√2 x + c is a tangent to the circle x²+y²=16, Find the value of c.

7. Find the center and radius of the following:

i)x²+(y+2)² = 0

ii) x²+y²+6x-4y+4 = 0

iii) x²+y²-x+2y-3 = 0

iv) 2x²+2y²-6x+4y+2 = 0

8. Find the equation of the parabola with focus (-√2,0) and directrix x=√2 .

9. Find the equation of the parabola whose vertex is (5,-2) and focus (2,-2)

10. Find the equation of the ellipse with foci (±2,0), vertices(±3,0).

11. Find the equation of the hyperbola with vertices (0,±4) and foci (0,±6)

12. Find the vertices ,foci for the hyperbola 9x²-16y²= 144

13. Find the equation of the parabola in each of the cases given below:

i) focus (4,0) and directrix x = -4 

ii) passes through (2,-3) and symmetric about y axis .

iii) vertex (1,-2) and (4,-2) iv) end points of latus rectum (4,-8) and (4,8).

14. Find the equation of the hyperbola in each of the cases given below:

i) foci (±2 , 0) eccentricity = 3/2

ii) centre (2,1) one of the foci(8,1) and corresponding directrix x=4.

15. Find the vertex, focus , equation of the directrix and length of the latus rectum of the following:

i) y² =16x²

ii) x² = 24y

iii) y² = -8x

iv) x² + 2x + 8y + 17 = 0

v) y² - 4y – 8x + 12 = 0

16. Find the equations of tangent and normal to the parabola x²+ 6x +4y + 5 = 0 at (1,3).

5 Mark Questions

1. Find the equations of tangent and normal to the parabola x²+4y²=32 when θ = π/4 .

2. Find the equations of the tangent and normal to hyperbola 12x²–9y²=108 at θ = π/4 .

3. Prove that the point of intersection of the tangent at ‘t1’ and ‘t2’ on the parabola y²=4ax is

 [at1t2 , a(t1+t2)]

4. If the normal at the point ‘t1’ on the hyperbola y²=4ax meets the parabola again at the point ‘t2’ then prove that t2 = (t1 + 2/t1)

5. Find the vertex , focus, directrix and length of the latus rectum of the hyperbola X²–4x–5y–1=0.

6. Find the equation of the ellipse whose eccentricity is 1 one of the foci is (2,3) and a directrix is x=7. Also find the length of the major and minor axis of the ellipse.

7. Find the foci,vertices and length of major and minor axis of the conic 4x²+36y²+40x-288y+532=0.

6. Identify the type of conic and find centre, foci, vertices and directrix of each of the following :

i) 18x² + 12y² - 44x +48y +120 = 0

ii) 9x² – y² – 36x -6y +18 = 0

7. Parabolic cable of a 60m portion of the roadbed f a suspension bridge are positioned as shown below. Vertical cables are to be spaced every 6m along this portion of the roadbed . Calculate the lengths of first two of these vertical cables from the vertex.

8. For the ellipse 4x²+y²+24x–2y+21=0, find the centre ,vertices and the foci also prove that length of latus rectum is 2.

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