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Syllabus

Find the coordinates of foot of perpendicular from the point (2,3) to the line 3x+4y+8=0.

Q.17 of miscellaneous ex. of N cert book chapter 10 st. line

The base of the equilateral triangle has an equation of x+2y=3 and one of the vertex is (1,1).find the equation of other two sides

find the equation of the line through the intersection of the lines 2x+3y-4 = 0 and x-5y = 7 that has its intercept equal to -4.

the equation of the perpendicular bisectors of sides AB and AC of a triangle ABC are x-y+5=0 and x+2y=0respectively. if the point is A (1,-2), find the equation of line BC.

Two adjacent sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0.

If the equation of one of the diagonals is 11x + 7y = 4, find the equation

of the other diagonal.

if a^2 + b^2 - c^2 - 2ab = 0 , then family of st. lines ax+by+c=0 intersects at which point(s)?

sir, can u explain me how to find tan inverse in log books..

Find the eq. of the straight lines which go through the origin and trisect the portion of the straight line 3x+y=12 which is intetercepted between the axes of the coordinates.

A line is such that it's segment between the lines 5x-y+4=0 and 3x+4y-4=0 is bisected at the point (1,5) obtain it's equation?

Find the equations of the lines which pass through (4,5) and make equal angles with lines 5x-12y +6 =0 and 3x-4y-7=0

find the coordinates of the incentre and centroid of the triangle whose sides have the equation 3x -4y=0, 12y+5x=0, y-15=0.

also please tell me what is incentre, circumcentre, orthocentre and centroid in a triangle

two sides of an isocesle triangle are given by the equation 7x-y+3=0 and x+y-3=0. if its third side passes through the point (1,-10) then its equations are-

The hypotenuse of a right angled triangle has its ends at points

(1,3)and(-4,1).Find the equation of the legs (perpendicular sides) of the triangle.Find the image of the point (1,2) in the line x-3y+4 =0

Find the equation of a line on which perpendicular from the origin makes an angle of 30 degree with the x-axis and which forma a triangle of area 50/3^1/2 with the coordinate axes ?

NCERT - miscellaneous exercise ch 10 Q-17

The end points of the hypotenuse of a right angled triangle are (1,3) and (-4,1). Find the equation of the legs of the triangle.

the distance of the point (3,5) from the line 2x +3y - 14 = 0 measured parallel to the line x - 2y = 1 is ?

a) 7/ root 5

b) 7/ root 13

c) root 5

d) root 13

A ray of light passing through the point (1, 2) reflects on the

x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.Find points on the line x + y + 3 = 0 that are at a distance of 5 units

from the line x + 2y + 2 = 0

Show that the points A(7,10), B(-2,5) and C(3,-4) are the vertices of an isoceles right-angled triangle.

Find the equation of a straight line which are parallel to x+7y+2=0 and at a unit distance from point (1,-1)

The area of the triangle formed by the coordinate axes and a line is 6 square units and the length of the hypotenuse is 5 units . Find the equation of the line

1. find the equation of perpendicular bisectors of the line segment joining the points (1,1) and (2,3)

2. Find the eq of the line which passes through the points (3,4) and the sum of its intercepts on the axes 14

One side of a rectangle lies along the line 4x + 7y + 5 = 0. Two of its

vertices are (–3, 1) and (1,1). Find the equation of other three sides.

Find the orthocentre of the triangle the equation of whose sides are x+y=1, 2x+3y=6, 4x-y+4=0

2. The eqn of base if an equilateral triangle is x+y-2=0 and the opposite vertext has co-ordinates (2,-1) find the area of the triangle.

if A(1,4) B(2,-3) C(-1,-2) are the vertices of a triangle ABC. find

a) the equation of the median through A

b) the equation of altitude through B

c) the right bisector of BC

find the equation of the line passing through the point of intersection of two lines x-3y+1=0 2x+5y-9=0 and whose distance from the origin is 5

^{1/2 .}orthocentre of a triangle whose sides are given by 4x-7y+10= 0 ,x+y-5=0 and 7x+4y-a5=0 is ??a) (-1, -2) b) (1, -2) c) (-1, 2)d) (1, 2)

if the image of the point(2,1) with respect to a line mirror be (5,2), find the equation of the mirror.

Find the coordinates of the point(s) on the line x+y+3=0, whose distance from the line x+2y+2 = 0 is 5

^{0.5}.Consider a family of straight lines (x + y) + lambda(2x - y + 1) = 0. Find the equation of the straight line belonging to this family that is farthest from (1, -3).

Kindly please don't refer me the link to a similar question that ha s already been answered as I tried that method but I got a wrong answer.

Thank You.

A line passes through a point A(1,2) and makes an angle of 60degree with x-axis and intersects line x+y=6 at point P.find AP.

the diagonal of a square lies along the line 8x-15y=0 one vertex is (1,2). find equations to the side of square passing through it?

Find equation of medians of triangle ABC whose vertices are A(2.5) B(-4,9) C (-2,-1)

find the equation of the line passing through the point (7,9)and which is such that the portion of it b/w the axes is divided by the point in the ratio 3:1

Find the slope of the line, which makes an angle of 30° with the positive direction of

y-axis measured anticlockwise.what difference it will get when it become clockwise in place of aticlockwise.

prove that the perpendicular drawn from the point (4,1) on the join of (2,-1) and (6,5) divides it in the ratio 5:8.

How to split a pair of line equation of ax

^{2}+2hxy+by^{2}+2gx+2fy+c=0 in the short method?find the equation of a straight line on which the perpendicular from the origin makes an angle of 30 degree with the x-axis and which forms a triangle of are 50/root3 with the axes.

find the equation of the straight line which cuts off intercepts on x axis twice that on y axis and is at a unit distance from the origin

a) reflection about the line y=x

b) transformation through a dist.2units along the +ve direction of the x-axis

c)rotation through an angle 45 deg about the origin in d anticlockwise direction . the final position of the point is given by the coordinates?

Find the equation of bisector of angle A of triangle whose vertices are A(4,3) , B(0,0) & C(2,3)

find the distance of the point (2,3) from the line 2x-3y+9=0 measured along a line making an angle of 45degreewith the x axis

if G is the centroid and I the incentre of the triangle with vertices A(-36,7) ,B(20,7) ,C(0,6) then find the value of GI?

find what the following equation becomes when the origin is shifted to the point(1,1)

x

^{2}+xy-3y^{2}-y+2=0show that area of a triangle formed by lines y=m

_{1}x , y=m_{2}x and y=c is equal to c^{2}/4 (√33 +√11) where m_{1}and m_{2}are the roots of the equation x^{2}+(√3 +2 )x +√3 - 1 =0Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line

x–2y= 3.If the co-ordinates of a variable point P be (acostheta,bsintheta) where theta is a variable quantity, find the locus of P.

Equation of two sides of a triangle are 3x-2y+6=0 and 4x-5y-20=0 and the orthocenter is (1,1). Find the equation of the third side.

find the equation of passing through the point (3,2) and whose slope is 3/4. find the coordinates of the points on the same line that are 5 units away from the point (3,2)

i) touches the X axis

ii) lies entirely inside the circle x^2 + +y^ = 18

a straight line makes an intercept on the y axis twice as long as that on the x axis and is at a unit distance from the origin.determine its equation (pls slove it)If

pandqare the lengths of perpendiculars from the origin to the linesxcosθ–ysinθ=kcos 2θandxsecθ+ycosecθ=k, respectively, prove thatp^{2}+ 4q^{2}=k^{2}if line joining A (2,0) AND B(3,1) is rotated abt A in anticlockwise direction thru an angle 15 . find equation of the line in new position

The line l has intercepts 'a' &'b' on the coordinate axis. The coordinate axes are rotated through a fixed angle,keeping origin fixed.If 'p'&'q' are the intercepts of the line

on the new axes , then 1/aL^{2}-1/p^{2}+1/b^{2}-1/q^{2}is equal to :If the liner 2x+y-3=0,5x+ky-3=0and 3x-y-2=0 are concurrent, find the value of k????? please tell me in detail how we will solve this question and what is the meaning of concurrent??????

If p and q are the lengths of perpendicular from the origin to the lines.

x cos theta- y sin theta = k cos 2 theta , and xsec theta + y cosec theta = k respectively, prove thatp^2 + 4q^2 = k^2If (1,2) and (3, 8) are a pair of opposite vertices of a square, find the

equation of the sides and diagonals of the square.