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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.

i) touches the X axis

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

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 circle which passes through the points P(1,0), Q(3,0) and R(0,2). Find also

(i) The coordinates of the other point in which the axis of y cuts the circle,

(ii) The coordinates of the other end of diameter through Q.

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?

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-

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

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 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.

If origin is shifted to (2, 3), then what will be the new coordinates of

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

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.

^{1/2}= (x+2y-5)/n. Find n ?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 to the straight line which passes through the point of intersection of the line 3x+4y-1=0 and 5x+8y-3=0 and is perpendicular to the line 4x-2y+3=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

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

a point p (x y) moves so that the sum of the distances from p to the coordinates axes is equal to the distance from p to the point A91,1). the equation of the locus of p in the first quadrant will be ?

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.

Ans (5,6) or(3,4)

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

the straight line y=m1x+c1,y=mx+c2,and x=0 intersect in the pointsP,Q and R.find the area of the triangle PQR..WHAT IS THE VALUE OF THE AREA IF C1=C2?

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.

Suppose that three lines have same y-intercept and that their slopes are 1/3 , 1/5 , 1/7. If the sum of x-intercept of the lines is 1000m, then heir common y-intercept , is equal to

(A) 200/3

(B) 3/200

(C) -3/200

(D) -200/3

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 straight line whose intercepts on the axes are thrice as

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?

triangle is formed by joning three lines x+y-6=0,3y-x+2=0 and 3y=5x+2?find the orthocenter of the triangle?

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

How to split a pair of line equation of ax

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

^{2},2at1)(at2^{2},2at2).Prove that t18t2=-1?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 lies midway between the lines 2x+3y+7=0 and 2x+3y+5=0find 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 locus of a point equidistant from the lines x+y+4=0 and 7x+y+20=0.

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

x–2y= 3.Q. A straight line x/a - y/b = 1 passes through the point (8,6) and cuts off a triangle of area 12 units from the axes of co-ordinates. Find the equations of the straight line.

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 sides of a triangle are given by the equation 3x+4y=10,4x-3y=5, and 7x+y+10=0. Show that the origin lies within the triangle.

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}Solution:Let BD be the bisector of $\angle $ABC. Then, AD : DC = AB : BCand AB = ${\sqrt{{\left(5+1\right)}^{2}+\left(1+7\right)}}^{2}=10$

BC = ${\sqrt{{\left(5-1\right)}^{2}+\left(1-4\right)}}^{2}=5$

∴ AD : DC = 2 : 1

By section formula, D $\equiv $( 1/3, 1/3)

Distance BD $\sqrt{{\left(5-\frac{1}{3}\right)}^{2}+{\left(1-\frac{1}{3}\right)}^{2}}=\frac{10\sqrt{2}}{3}$.

How did they come up with the first conclusion? AD:DC=AB:BC

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 ?

(A) 4 (B) 5 (C) 6 (D) 9.25

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

6. Let a given line L

_{1}intersect the x and y-axes at P and Q respectively. Let another line L_{2}perpendicular to L_{1}, cut the x and y-axesat R and S, respectively. Show that the locus of the point of intersection of the lines PS and QR is a circle passing through the origin.

11. Let ABC be a triangle with AB = AC. If D be the mid point of BC, the foot of the perpendicular drawn from D to AC and F

the mid point of DE, prove that AF is perpendicular to BE.

(A) 3x = 4y (B) y = 2x (C) x = 3y (D) None