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

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

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

Q. Find the equation of perpendicular bisector of the line segment joining (1, 1) & (2, 3)

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 point P is the foot of the perpendicular from A(0,t) to the line whose equation is y=tx. Determine

a) the equation of line AP

b) the co-ordinate of P

c) the area of triangle OAP, where O is origin

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.

Reduce the equation into intercept form3x+4y-12=0(i) Find the distance of the above line from the origin.(ii) Find the distance of the above line from the line. 6x+8y-18=0

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.

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?

proove that the lines 3x-4y+5=0 ,7x-8y+5=0 and 4x+5y=45 are concurrent also find the point of concurrency

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

If the origin is shifted to the point (2,-1) obtain the new equation of locus,axes remainng parallel.The old equation of locus is:

2x²-3xy-9y²-5x-24y-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.

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

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

9. A stick of length 10 units rests against the floor and a wall of a room.

If the stick begins to slide on the floor then the locus of its middle points -

(A) x

^{2 }+ y^{2}= 2.5(B) x

^{2}+ y^{2}= 25(C) x

^{2}+ y^{2}= 100(D) none

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.

^{2}and x^{2}+ y + 1 = 0 will be –^{2}xcosθ+ysin = p

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.^{ 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

Q.24. (B) If line 2x - by + 1 = 0 intersects the curve $2{x}^{2}-b{y}^{2}+\left(2b-1\right)xy-x-by=0$ at points A & B and AB subtends a right angle at origin, then value of $b+{b}^{2}$ is equal to

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 line passing through the point of intersection of lines 4x + 7y=3 and 2x-3y+9=0,that has equal intercepts on the axes

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 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.

^{2 }-3(mx-ly)^{2 }and lx+my+n=0 form an equlateral triangle with area n^{2}/root3(l^{2}+m^{2})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.

find the equation of the straight line passing through the points of intersection of 2x+y-1=0 and x+3y-2=0 and making with the coordinate axes a triangle of area 3/8 sq.units

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?

Show that the points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are collinear.

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

_{1,}y_{2}) and (h,k). if slope of the line is m , show that k-y_{1}=m(h-x_{1})How to split a pair of line equation of ax

^{2}+2hxy+by^{2}+2gx+2fy+c=0 in the short method?the coordinates of a point which is at a distance of 1/root2 units from (1,1) in the direction of line x + y - 3= 0answer is (1/2, 3/2)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 equation of the lines through the point of intersection of the lines x-3y+1=0 and 2x+5y-9=0 whose distance from the origin is sqrt(5)

(i) 2x+3y-4=0 and 2x+3y+17=0

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 which is parallel to the line 2x-3y=5 and is such that sum of its intercepts on the axes is 6

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

x

^{2}+xy-3y^{2}-y+2=0if 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 the lines through the point (3, 2) which make an angle of 45° with the line

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

the points A,Band C are(4,0),(2,2),and(0,6) respectively.AB produced cuts the y-axis at Pand CB produced cuts the x-axis at Q.find the co-ordinates of the pointsP and q.Find the eq. of the straight line joining the mid points of AC nad OB( Where O is the origin )and verify that this line passes through the mid point of PQ.

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)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

the base of an equilateral triangle with side 2a lies along y-axis such that the midpoint of the base is at the origin.find the vertices of the triangle.