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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

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

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

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 coordinates of three points O,A,B are (0,0), (0,4), (6.0) respectively. A point P moves so that the area of the triangle POA is twice the area of the traingle POB. Find the equation to both parts of the locus of P.

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

^{2}+ 5xy + 3y^{2}+ 7y - 98 = 0 is tan^{-1}m then m equals totwo 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-

How to split a pair of line equation of ax

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

Thank You.

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 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

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 line through point (m,-9) and (7,m) has slope m.the y intercept of this line is?????

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

Let the algebric sum of the perpendicular distances from the point (2,0), (0,2) and (1,1) to a variable line be 0. Then show that the line passes through a fixed point.

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

(And:8h^2=9ab)

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.

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.A) P lies on the straight line 3x+4y=36

B) P lies on any line perpendicular to AB

C) P lies on the right bisector AB

D) P lies on the circle passing through the points (1,2) and (7,10) and having a radius of 10 units.

IT IS MULTICORRCT QUESTION

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

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

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.

the inclination of the straight line passing through the point ( -3,6) and the midpoint of the line joining the point (4,-5) and (-2,9) is

A(a) (-11, -1) (B) (11,1) (C) (11, -1) (D) (-10,1)

^{2}and x^{2}+ y + 1 = 0 will be –if the image of the point(2,1) with respect to a line mirror be (5,2), find the equation of the mirror.

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 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.

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?

^{2}+1/b^{2}= 1/c^{2}, where c is a constant. the locus of the foot of the perpendicular from the origin on the given line is x^{2}+ y^{2}= c^{2.}Find the equation of bisector of angle A of triangle whose vertices are A(4,3) , B(0,0) & C(2,3)

Area of the quadrilateral formed by lines |x| +|y|=2 is?

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 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

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

x

^{2}+xy-3y^{2}-y+2=0the 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.

Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line

x–2y= 3.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?

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.

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)

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}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)_{1 }and r_{2}are both touching the coordinate axes and intersecting each other orthogonally. The value of r_{1/}r_{2}(where r_{1}>r_{2}) equalsA) 2+root 3

B) root 3+1

C) 2-root 3

D) 2+root 5

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 ?

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

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

find the eqn of the line cutting off an intercept -2 from the y-axis and equally inclined to the axes.

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

One 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