Search Colleges, Courses, Exams, Questions and Articles

Ask a query on 8879100846 Ask Login | Sign Up

 

 

› Ask & Answer › Question

Consider a triangle having vertices A ( − 2 ,     3 ) ,     B ( 1 ,     9 )     a n d     C ( 3 ,     8 ) .  If a line L passing through the circum-center of triangle ABC, bisects line BC, and intersects y-axis at point ( 0 , α 2 ) ,  then the value of real number a is…………..

0 2 Views | Posted a month ago
Asked by Shiksha User

  • 1 Answer

  • V

    Answered by

    Vishal Baghel | Contributor-Level 10

    a month ago

    ( 5 0 ) 2 = ( 4 5 ) 2 + ( 5 ) 2

    ∴ ∠ B = 9 0 ° circum centre = O ( 1 2 , 1 1 2 )

    Mid point of BC = D ( 2 , 1 7 2 )

    Equation of OD is y = 2x + 9 2 . This line passes through

    ( 0 , α 2 ) ∴ α = 9

Similar Questions for you

A line passes through (9, 0), making angle 30° with positive direction of x-axis. It is rotated by angle of 15° with respect to (9, 0). Then one of the equation of new line is
A
alok kumar singh

Eqn : y – 0 = tan45° (x – 9) Þ y = (x – 9)

Option (B) is correct

If two circle x2 + y2 = 4 and x2 + y2 – 4lx + 9 = 0 intersect at two distinct points, then find the range of l.
A
alok kumar singh

|r1 – r2| < c1c2 < r1 + r2

-> | 2 − 4 λ 2 − 9 | < | 2 λ | < 2 + 4 λ 2 − 9

| 2 λ | − 2 < 4 λ 2 − 9    

4 λ 2 + 4 − 8 | λ | < 4 λ 2 − 9

  λ > 1 3 8 ,   λ < − 1 3 8           

4 λ 2 − 9 > 0

λ > 3 2 ,   λ < − 3 2

λ ∈ ( − ∞ ,   − 1 3 8 ) ∪ ( 1 3 8 ,   ∞ )           

Now,

| 2 − 4 λ 2 − 9 | < | 2 λ |            

4 + 4 λ 2 − 9 − 4 4 λ 2 − 9 < 4 λ 2  

4 4 λ 2 − 9 > − 5 ⇒ λ ∈ R  

λ ∈ ( − ∞ ,   − 1 3 8 ) ∪ ( 1 3 8 ,   ∞ )  

The line passes through the centre of circle x2 + y2 – 16x – 4y = 0, it interacts with the positive coordinate axis at A & B. Then find the minimum value of OA + OB, where O is origin.
A
alok kumar singh

(y – 2) = m (x – 8)

⇒   x-intercept

⇒     ( − 2 m + 8 )

⇒   y-intercept

⇒   (–8m + 2)

⇒   OA + OB = − 2 m 2  + 8 – 8m + 2

f ' ( m ) = 2 m 2 − 8 = 0  

-> m 2 = 1 4

-> m = − 1 2

-> f ( − 1 2 ) = 1 8

->Minimum = 18

The image of the point (3, 5) in the line x – y + 1 = 0, lies on:
V
Vishal Baghel

Kindly consider the following figure

A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of the line on the coordinate axes is 1 4 .  Three stones A, B and C are placed at the point (1, 1), (2, 2) and (4, 4) respectively. Then which of these stones is / are on the path of the man?
V
Vishal Baghel

According to question,

1 2 ( 1 a + 1 b ) = 1 4

1 a + 1 b = 1 2 . . . . . . . . ( i )

Equation of required line is x a + y b = 1

Obviously B (2, 2) satisfying condition (i)

Get authentic answers from experts, students and alumni that you won't find anywhere else

Sign Up on Shiksha

On Shiksha, get access to

  • 65k Colleges
  • 1.2k Exams
  • 688k Reviews
  • 1800k Answers

Learn more about...

Share Your College Life Experience

Write a Review

Didn't find the answer you were looking for?

Search from Shiksha's 1 lakh+ Topics

or

Ask Current Students, Alumni & our Experts

Ask Now
Community GuidelinesUser Points System
QuestionsDiscussionsTags
×

This website uses Cookies and related technologies for the site to function correctly and securely, improve & personalise your browsing experience, analyse traffic, and support our marketing efforts and serve the Core Purpose. By continuing to browse the site, you agree to Privacy Policy and Cookie Policy.

Need guidance on career and education? Ask our experts

Characters 0/140

The Answer must contain atleast 20 characters.

Add more details

Characters 0/300

The Answer must contain atleast 20 characters.

Keep it short & simple. Type complete word. Avoid abusive language. Next

Your Question

Edit

Add relevant tags to get quick responses. Cancel Post