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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 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.

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?

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.

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 :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

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 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.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 image of the point (1,2) in the line x-3y+4 =0

Q. Example 77: Let A

_{0}_{ }A_{1}_{ }A_{2}_{ }A_{3}_{ }A_{4}_{ }A_{5}be a regular hexagon inscribed in a circle of unit radius then the product of the lengths of the line segments A_{0}A_{1}, A_{0}A_{2}and A_{0}A_{4}is(a) 3/4 (b) $3\sqrt{3}$

(c) 3 (d) $3\sqrt{3}$/ 2

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.

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 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

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.

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

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

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

The sides AB and AC of a triangle ABC are 2x + 3y=29 and x + 2y=16 respectively. If the mid-point of BC is (5,6) then find the equation of BC.

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.

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 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?

(And:8h^2=9ab)

the point P(a,b) lies on the straight line 3x+2y=13 and the point Q(b,a) lies on the straight line 4x-y=5, then the equation of line PQ 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.

How to split a pair of line equation of ax

^{2}+2hxy+by^{2}+2gx+2fy+c=0 in the short method?find what the following equation becomes when the origin is shifted to the point(1,1)

x

^{2}+xy-3y^{2}-y+2=0find 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). (- infinity, 3) U (9/2, infinity)

b). (3, 9/2)

c). (-infinity, 3)

d). (9/2, infininity)

A line through through the point (3,0) meet the variable line y=tx at rt angle at the point P. Find in terms of t, the co-ordinates of P

find tje co-ordinate of P

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

23) If one vertex of an equilateral triangle of side 'a' lies at the origin and the other lies on the line $x-\sqrt{3}y=0,$ then the coordinates of the third vertex are :

(A) (0, a) (B) $\left(\frac{\sqrt{3}a}{2},-\frac{a}{2}\right)$ (C) (0, -a) (D) $\left(-\frac{\sqrt{3}a}{2},\frac{a}{2}\right)$

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

x–2y= 3.Thank You.

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

^{1/2}units. The area enclosed by the locus of the point is?Thank You.

No links Please!!!

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)The number of possible straight lines,passing through (2,3) and forming a triangle with coordinate axes, whose area is 12 sq. units is -

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??????

7. Equation of two equal sides of a triangle are the lines 7x + 3y - 20 = 0 and 3x + 7y - 20 = 0 and third side passes through the point (-3,3) then the equation of third side can be-

(A) x + y = 0

(B) x - y + 6 = 0

(C) x + 3 = 0

(D) y = 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}1). lies on same side of lines

2). lies on one of the lines

3). lies on different sides of lines

4). lies between the lines

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

^{2}+4xy -py^{2}+4x+qy+10= 0 will represent two mutually perpendicular straight lines, if(A) p= 1 and q = 2 or 6 (B) p= 2 and q = -2 or 8 (C) p= 2 and q = 0 or 8 (D) p= 2 and q = 0 or 6

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^2find 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)

find the coordinate of the foot of perpendicular form of point (-1,3)to the line(3x-4y-16)=0

show 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 circle passing through the points (1,2), (3,-4) and (5,-6)