Скачать или смотреть Tangent & Normal to the circle (Part-4)Class 12 Solution of old is gold neb plant and animal science

Solution of old is gold Class XII TVET NEB
Analytical Geimetry
Tangent and Normal

15. 2076 Set C Q.No. 9a Find the condition that the line px + qy = r is tangent to the circle x²+ y² = a².

Ans: a ^ 2 * (p ^ 2 + q ^ 2) = r ^ 2

16. 2075 GIE Q.No. 4b Find the equation of the circle whose center is at (-3,-4) and touches the x-axis.

Ans: x ^ 2 + y ^ 2 + 8x + 8y + 9 = 0

17. 2075 GIE Q.No. 9a Find the equation of the circle having the chord x - y - 1 = 0 of the circle 2x ^ 2 + 2y ^ 2 - 2x - 6y - 25 = 0 as diameter.

Ans: x ^ 2 + y ^ 2 - 3x - y - 10 = 0

18. 2075 Set A Q.No. 4b If one end of a diameter of circle x ^ 2 + y ^ 2 - 2x + 6y - 15 = 0 (4, 1), find the coordinate of the other end.

Ans: (-2,-7)

19. 2075 Set A Q.No. 9a Find the value of k if the length of the tangent from the point (1, 2) to the circle x ^ 2 + y ^ 2 + x + y - 4 = 0 and 3x ^ 2 + 3y ^ 2 - x - y - k = 0 are in the ratio 4:3.

Ans: 21 4

20. 2075 Set B Q.No. 4b Find the equation of the circle which touches both axes and has radius 4 units.

Ans: x ^ 2 + y ^ 2 - 8x - 8y + 16 = 0

21. 2075 Set B Q.No. 9a Find the condition that the line k + my + n = 0 should be tangent to the circle x ^ 2 + y ^ 2 + 2gx + 2fy + c = 0

Ans: (n - lg - m*Omega) ^ 2 = (l ^ 2 + m ^ 2)(g ^ 2 + l ^ 2 - c)

22. 2075 Set C Q.No. 4b Find the equation of the circle which touches both the axes and has its centre on the line x - 2y = 3

Ans: x ^ 2 + y ^ 2 + 6x + 6y + 9 = 0

23. 2075 Set C Q.No. 9a Find the equations of the tangent to the circle x ^ 2 + y ^ 2 - 6x + 4y = 12 which are parallel to the line 4x + 3y + 5 = 0

Ans: 4x + 3y - 31 = 0

24. 2074 Supp Q.No. 9al Prove that the straight line y = x + a * sqrt(2) touches the circle x ^ 2 + y ^ 2 = a ^ 2 Also find the point of contact.
25. 2074 Set A Q.No. 9a Find the equations of the tangent and normal to the circle x ^ 2 + y ^ 2 - 2x - 4y + 3 = 0x (2, 3).

26. 2074 Set B Q.No. 4b Find the equation of the circle which touches the x-axis at (4,0) and passes through the point (1, 1).

Ans:xy-x-10y+18

27. 2074 Set B Q.No. 9 Find the conditions for the circles x ^ 2 + y ^ 2 = a ^ 2 * i (x-c)+y²=bl touch (i) externally(ii) internally.

Ans: abc-b

20. 2073 Supp Q.No. 4o Find the equation of the tangent to the circle x ^ 2 + y ^ 2 - 2x - 4y + 3 = 4x (2.3).

29. 2073 Supp Q.No. 9a Find the equation of a circle passing through the points (1, 2), (3, 1) and (-3,-1).

x / (x ^ 2) + y ^ 2 - x + 2y - 12xy

30. Find the equation to the circle which touches aves at(a, 0) * ard(0, a)

Ans:x+y-24-2ay touches the circle

31. what value of 'a', the x + 3y = a [2473 5et subset2.10.9y]F x ^ 2 + y ^ 2 - 3x - 3y + 2 = 0 . Find also the point of contact

Ans: (1, 0) and (2, 2)

32. 2073 Set D Q.No. 4b Find the equation of the circle touching x-axis whose center is at (4.3).

subset x ^ 2 + y ^ 2 - 2x - 3y + ||x||

31. 2073 Set D Q.No. sa Find the condition that the line bx + my + n = 0 to the circlex+y² + 2gx2ly+c=0.

Ans: (n-lg-mf-mf-

34. 2072 5at subset Q.N0.49] sqrt(p ^ 2 + q ^ 2) . Find the equation of the circle with centre at (p, q) and radius

Ans: x ^ 2 + y ^ 2 - 2px - 2qx + 1

35. 2072 Set C Q.No. 9a Find the equation of the tangent to the circle x ^ 2 + y ^ 2 = z ^ 2 * a the point (x, y)

36. 2072 Set D Q.No. 9a Show that the line x/a + y/b = 1 will be tangent to the circle 111 (x-a)+(y-b)=

37. the equation of a circle concentric with the cide boxed 2972 5et E 0.86.49 x ^ 2 + y ^ 2 + 2x + 6y - 39 = 0 ... passing through (7, -7).

38. 2072 Set E Q.No. Sa Find the equations of the circle and tangent to the cirde perpendicular to the diameter whose end points are (3-4) and (-4,-3).

x / x + 7y plus/minus 25 + 1

39. 2071 Supp. Q.No. Sa Find the value of k if the line 4x - 3y + k = 0 is tangent to the circle x ^ 2 + y ^ 2 - 8x + 12y + 3 = 0

Ans: 1 or

40. 2071 Set C Q.No. 4b Find the equation of the circle which touches the axes (2.0) and (0, 2).

41. 2071 Set C Q.No. Bal Prove that the tangents to the circle x ^ 2 + y ^ 2 = 5 the point (1,-2) also touches the circle x ^ 2 + y ^ 2 - 8x + 6y + 20 = 0
42. 2071 Set D Q.No. 4b Find the equation of the circle whose center is at (3, 4) and touches the x-axis