Home
Class 11
MATHS
Let a x+b y+c=0 be a variable straight l...

Let `a x+b y+c=0` be a variable straight line, where `a , ba n dc` are the 1st, 3rd, and 7th terms of an increasing AP, respectively. Then prove that the variable straight line always passes through a fixed point. Find that point.

Promotional Banner

Similar Questions

Explore conceptually related problems

If a , b ,c are in harmonic progression, then the straight line ((x/a))+(y/b)+(1/c)=0 always passes through a fixed point. Find that point.

If aa n db are two arbitrary constants, then prove that the straight line (a-2b)x+(a+3b)y+3a+4b=0 will pass through a fixed point. Find that point.

If non-zero numbers a, b, c are in H.P., then the straight line (x)/(a)+(y)/(b)+(1)/(c)=0 always passes through a fixed point. That point is

Find the normal to the curve x=a(1+costheta),y=asinthetaa tthetadot Prove that it always passes through a fixed point and find that fixed point.

If 5a+5b+20 c=t , then find the value of t for which the line a x+b y+c-1=0 always passes through a fixed point.

Let A B C be a given isosceles triangle with A B=A C . Sides A Ba n dA C are extended up to Ea n dF , respectively, such that B ExC F=A B^2dot Prove that the line E F always passes through a fixed point.

A straight line passes through (1,2) and has the equation y-2x-k =0 . Find k.

If a, b, c are in AP then ax + by + c = 0 will always pass through a fixed point whose coordinates are

Find the point where the straight line passes through (6,7,4)and(8,4,9) cut the xz and yz planes.

From a variable point on the tangent at the vertex of a parabola y^2=4a x , a perpendicular is drawn to its chord of contact. Show that these variable perpendicular lines pass through a fixed point on the axis of the parabola.