Straight Lines

Question 1

Perpendicular distance of a point from a line

Line: ax+by+c
Point: (h, k)

Answer 1

D = (|ah+bk+c|) /√( a^2 + b^2 )

Question 2

Distance between parallel lines

L1: ax+by+c1
L2:ax+by+c2

Answer 2

D=| C1 - C2 / √( a^2 +b^2) |

Question 3

When the general coordinate (x, y) axes is rotated by an angle theta then the new coordinate of (X, Y) is ?

Answer 3

X= x cos theta + y sin theta
Y= -x sin theta + y cos theta

Method to remember:
x | y |
X | cos theta | sin theta |
Y | -sin theta | cos theta |

Differentiation hua hai cos and sin ka upar se

Question 4

For an equilateral triangle point C (x1, y1) point B (x2, y2) & point P (h, k) then value of (h, k)=?

Answer 4

H = {x1 + x2 +- √3 ( y1- y2 )} / 2
K = {y1 + y2 -+ √3( x1- x2)} / 2

Question 5

Relation between orthocenter (H) , centroid (G) , circumcenter (O)

Answer 5

HG:GO = 2:1 always

Question 6

Slope of line ax+by+c :

Answer 6

-a / b
Or we can say
- coefficient of x / coefficient of y

Question 7

For the perpendicular line of ax+by+c=0 equation becomes ?

Answer 7

bx - ay + c = 0

The coefficient of a & b interchanged and sign of y will be changed

Question 8

Let a point be (h, k) and it is passing through a line ax+by+c=0 and the coordinate of their contact is (l, m) then the coordinate image of (h, k)?

Without using formula coordinate of the image just using object coordinate (h, k) and the coordinate of foot of perpendicular (l, m)?

Answer 8

(L-h)/a = (m-k)/b = -(ah+bk+c) / a^2 + b^2

Assume coordinates to be alpha (a) and beta (b) so:

(a+h) / 2 = L & (b + k) /2 = m

Question 9

What does double intercept form mean:

Answer 9

When the x-intercept & y-intercept is given x intercept = a & y-intercept = b

X /a + y/b = 1

M2: x-intercept puche to put y=0 & jab y intercept puche then put x=0

Question 10

If a line is at whatever distance from the origin & another line is passing through the origin & is forming an angle alpha from the abscissa and is perpendicular to that line then find the equation of the first line

Answer 10

X cos alpha + y sin alpha = distance of the line from the origin

Question 11

Two points (h, k) & (x, y) lie on a straight line passing through the point & forming an angle theta with the abscissa the eqn. of that line is?

And if 1 point coordinate is only given such that (h, k) & distance between the points is r & and the point is in a straight line, the line is inclined at angle theta on the abscissa then the coordinate of the other point? ( phele wala question ka hi hai baat)

Answer 11

X-h /cos theta = y-k / sin theta = r

(h + r cos theta , k + r sin theta )