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Syllabus

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

P and Q are two variable points on the axes of X and Y respectively, such that OP+OQ = a. Find the equation of locus of the foot of perpendicular from thw origin on PQ.

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

(A) ${x}^{2}+{y}^{2}-5x+7y=0$ (B) ${x}^{2}+{y}^{2}+5x-7y=0$

(B) ${x}^{2}+{y}^{2}+5x+7y=0$ (C) ${x}^{2}+{y}^{2}-5x-7y=0$

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.

show that the four points (1,0),(2,-7),(8,1) and (9,-6) are concyclic

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 locus of the point P such that the sum of it's distances from (0,2) and (0,-2) is 6.

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?

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..

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-

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?

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

^{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.}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. 29/5 b.6 c.5 d.11/5

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.

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

the straight line passing through the point of intersection of the straight line x-3y+1=0 and 2x+5y-9=0 and having infinite slope and at a distance 2 unit from the origin has the 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

It is a Numerical based question

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) 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?

$ax+by+c=0;ax+by+c\text{'}=0;a\text{'}x+b\text{'}y+c=0a\text{'}x+b\text{'}y+c\text{'}=0$ are at right angles. Also find the equation to the diagonals of the parallelogram.

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)

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

^{2}+ 5xy + 3y^{2}+ 7y - 98 = 0 is tan^{-1}m then m equals toFind the orthocentre of the triangle the equation of whose sides are x+y=1, 2x+3y=6, 4x-y+4=0

Find K if (K,2 ) is an interior point of the triangle formed by the lines x+y=4, 3x-7y=8 and 4x-y=31.

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 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.

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.

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.

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.

If a vertex, the , circumcenter, and the centroid of a triangle are ( 0, 0 ), (3, 4) and (6, 8) respectively, then the triangle must be

a. a right angles triangle

b. an equilateral triangle

c. an isosceles triangle

d. a right-angled isosceles triangle

Sol: Clearly, ( 0, 0 ), (3, 4) and (6, 8) are collinear. So, the circumcenter M and the centroid G are on the median which is also the perpendicular bisector of the side. So the triangle must be isosceles.

How did we come to know they're on the median and also the perpendicular bisector? (I couldn't understand it through the triangle I plotted. Please make a figure if that makes things easier)

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?

segment PQ formed by joining the points P(4,2,-6) and

Q(10,-16,6).

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

A right angled triangle ABC having right angle at C, CA=b and CB=a, move such that the angular points A and B slide along x-axis and y-axis respectively. Find the locus of C.

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}.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 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) mx-nx=mn b) mx+ny=m c) nnx+my=n d) nx+ my=mn

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

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

x

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

^{2})^{1/2}+ t, 0] and B = [(1-t^{2})^{1/2}- t, 2t] are two variable points where t is a parameter, the locus of the middle point of AB isFind the equation of the lines through the point (3, 2) which make an angle of 45° with the line

x–2y= 3.Answer is 2 (explain)

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)For the variable triangle ABC with fixed vertex (1,2) and A,B having coordinates (cost,sint),(sint,-cost) respectively, Find the locus of its centroid.

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 ?

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

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

(Please solve it by using foot of the perpendicular)