Question

1. Transformer the equation

3 10 0 x y   

into Normal form.

2. Find the distance between the parallel lines

5 3 4 0, 10 6 9 0 x y x y      

3. Find the value of ‘K’ if

3 7 1 0 x y    , 7 3 0 x ky   

are perpendicular

4. Find the ratio in which the straight line

5 6 21 0 x y   

divides the line segment joining the points

(4, -1) and (2, 1)

SECTION - II 2 X 4 =8

Answer any two questions of the following. Each question carries 4 marks

5. Find the orthocenter of the triangle formed by the points (-5, -7) , (13, 2), (-5, 6)

6. If the acute angle between the lines

4x 7 0, 5 9 0       y kx y

is 450

, then find the value of K

7. If non-zero numbers a, b, c are in harmonic progression, then show that the equation

1

0

x y

abc

  

represents a family of concurrent lines and find the point of concurrency.

SECTION –III 2 X 7 = 14

Answer any two questions. Each question carries 7 marks

8. If (h, k) is the image of (x1, y1) with respect to the line

ax by c a b      0.( 0, 0)

then

 1 1  1 1

2 2

h x k y 2 ax by c

a b a b

    

 



. Find the image of (1, -2) with respect to the straight line

2x – 3y + 5 = 0.

9. Find the circumcentre of the triangle formed by the points (1, 3) (-3, 5) (5, -1)

10. A straight line through

Q( 3, 2)

makes an angle of

6



with x – axis in positive direction. If the

straight line intersects 3 4 8 0 at x y P    , find the distance PQ.​

Answer 1

2 = multiply 1 st eq by 2,both side

10x- 6y - 8 = 0

SO DISTANCE = 1/ √100+64

= 1√164

4 = By mid point formula

(x2+x/2)(y2+y/2)

2+4/2;1+-1/2

6/2;0/2

3;0=P

P(x,y)=mx2+m2x/m+m2, my2+M2Y1/m+m2

P(3,0)=K(2)+1(4)/K+1,K(1)+1(-1)/K+1

P(3,0)=2K+4/K+1,K-1/K+1

3=(2K+4)/K+1

3(K+1)=2K+4

3k+3=2k+4

3k-2k=4-3

k=1/1

k=1:1.