UrbanPro

Take Class 11 Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Search in

Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4x + y = 16.

Asked by Last Modified  

Follow 1
Answer

Please enter your answer

Let the equation of the required circle be (x – h)2 + (y – k)2 = r2. Since the circle passes through points (4, 1) and (6, 5), (4 – h)2 + (1 – k)2 = r2 … (1) (6 – h)2 + (5 – k)2 = r2 … (2) Since the centre (h, k) of the circle lies on line 4x + y = 16, 4h...
read more

Let the equation of the required circle be (xh)2 + (yk)2 = r2.

Since the circle passes through points (4, 1) and (6, 5),

(4 – h)2 + (1 – k)2 = r2 … (1)

(6 – h)2 + (5 – k)2 = r2 … (2)

Since the centre (h, k) of the circle lies on line 4x + y = 16,

4h + k = 16 … (3)

From equations (1) and (2), we obtain

(4 – h)2 + (1 – k)2 = (6 – h)2 + (5 – k)2

⇒ 16 – 8h + h2 + 1 – 2k + k2 = 36 – 12h + h2 + 25 – 10k + k2

⇒ 16 – 8h + 1 – 2k = 36 – 12h + 25 – 10k

⇒ 4h + 8k = 44

h + 2k = 11 … (4)

On solving equations (3) and (4), we obtain h = 3 and k = 4.

On substituting the values of h and k in equation (1), we obtain

(4 – 3)2 + (1 – 4)2 = r2

⇒ (1)2 + (– 3)2 = r2

⇒ 1 + 9 = r2

r2 = 10

Thus, the equation of the required circle is

(x – 3)2 + (y – 4)2 =

x2 – 6x + 9 + y2 ­– 8y + 16 = 10

x2 + y2 – 6x – 8y + 15 = 0

read less
Comments

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Recommended Articles

With the current trend of the world going digital, electronic renaissance is a new movement that is welcomed by the new generation as it helps makes the lives of millions of people easier and convenient. Along with this rapidly changing movement and gaining popularity of Internet, e-Learning is a new tool that emerging...

Read full article >

Learning for every child starts from a very young age. While the formal methods include school curriculums and private lessons, the informal methods include dancing, music, drawing, and various fun-filling activities. Playing games and practising these types of activities helps the children get out of boredom and...

Read full article >

E-learning is not just about delivering lessons online. It has a much broader scope that goes beyond manual paper or PowerPoint Presentations. To understand the reach of E-learning and how the whole process works in developing the Educational system, we will discuss a few points here. Let us find out how this new learning...

Read full article >

Quality education does not only help children to get a successful career and life, but it also hugely contributes to society. The formal education of every child starts from school. Although there are numerous schools, parents find it challenging to choose the right one that would fit their child. It is difficult for them...

Read full article >

Looking for Class 11 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you
X

Looking for Class 11 Tuition Classes?

The best tutors for Class 11 Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class 11 Tuition with the Best Tutors

The best Tutors for Class 11 Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more