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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

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

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.

If (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.

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.

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

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 ?

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?

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

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

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.

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

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

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.

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

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 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 equation of the lines which are at a distance root 3 units from the origin and pass through the point (2, 0)

Find points on the line x + y + 3 = 0 that are at a distance of 5 units

from the line x + 2y + 2 = 0

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

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

the equation of the base of a n equilateral triangle is x+y=2 and the vertex is (2,-1). Find the length of the side of the triangle.

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

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

area of triangle formed by the angle bisectors of the pair of lines x

^{2}-y^{2}+2y=1 and x+y=3 in square unit isOne side of a square makes an angle alpha with x-axis and one vertex of the square is at the origin, prove that equations of its diagonals are y(cos alpha - sin alpha) = x(sin alpha - cos alpha) and y(sin alpha + cos alpha) + x(cos alpha - sin alpha) = a

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.

find the equation of the line passing through the points (a cos alpha, asin alpha) and (acos beta, a sin beta)

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 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.

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}.i) touches the X axis

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

How to split a pair of line equation of ax

^{2}+2hxy+by^{2}+2gx+2fy+c=0 in the short method?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.

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 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.

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

Find the equation of the line through the intersection of lines 3x + 4y = 7 and x – y + 2 = 0 and

(Please solve it by using foot of the perpendicular)

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 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)

The equations of the two straight lines through (7,9) and making an angle of 60degree with the line x-3

^{1/2}y-2*3^{1/2}=0, are:Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line

x–2y= 3.Find equation of medians of triangle ABC whose vertices are A(2.5) B(-4,9) C (-2,-1)

If the co-ordinates of a variable point P be (acostheta,bsintheta) where theta is a variable quantity, find the locus of P.

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

x

^{2}+xy-3y^{2}-y+2=0a 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)Find the equation of the bisector of ∠A of ∆ABC whose vertices are A(4,3),B(0,0) and C(2,3).

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

find the equation of the line through the intersection of the lines x+2y-3=0 and 4x -y+7=0 and which is parallel to 5x +4y -20=0.

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??????

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 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^2